2x^2-20x=89=-87

Solution for 2x^2-20x=89=-87 equation:

2x^2-20x=89=-87

We move all terms to the left:

2x^2-20x-(89)=0

a = 2; b = -20; c = -89;
Δ = b2-4ac
Δ = -202-4·2·(-89)
Δ = 1112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1112}=\sqrt{4*278}=\sqrt{4}*\sqrt{278}=2\sqrt{278}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{278}}{2*2}=\frac{20-2\sqrt{278}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{278}}{2*2}=\frac{20+2\sqrt{278}}{4}
$