Consider the given quadratic equation that we have :
[tex]{:\implies \quad \sf -5x^{2}+5=-2x}[/tex]
Multiplying both sides by -1 will yield ;
[tex]{:\implies \quad \sf 5x^{2}-5=2x}[/tex]
Write the above quadratic equation in the form of standard quadratic equation ax² + bx + c = 0 ,
[tex]{:\implies \quad \sf 5x^{2}-2x-5=0}[/tex]
Now , comparing this with the standard form of quadratic equation we will get a = 5 , b = -2 , c = -5 . So now , Discriminant (D) = (-2)² - 4 × 5 × -5 = 4 + 100 = 104
Now , by the quadratic formula ;
[tex]{:\implies \quad \sf x=\dfrac{-(-2)\pm \sqrt{104}}{2\times 5}}[/tex]
[tex]{:\implies \quad \sf x=\dfrac{2\pm 2\sqrt{26}}{2\times 5}}[/tex]
[tex]{:\implies \quad \sf x=\dfrac{\cancel{2}(1\pm \sqrt{26})}{\cancel{2}\times 5}}[/tex]
[tex]{:\implies \quad \bf \therefore \quad \underline{\underline{x=\dfrac{1\pm \sqrt{26}}{5}}}}[/tex]
For any quadratic equation of the form ax² + bx + c , the Discriminant (D) is given by D = b² - 4ac , and the root [tex]\bf x[/tex] of the quadratic equation is given by the quadratic formula as
