2x^2+52x-90=0

Solution for 2x^2+52x-90=0 equation:

2x^2+52x-90=0

a = 2; b = 52; c = -90;
Δ = b2-4ac
Δ = 522-4·2·(-90)
Δ = 3424
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:

$\sqrt{\Delta}=\sqrt{3424}=\sqrt{16*214}=\sqrt{16}*\sqrt{214}=4\sqrt{214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-4\sqrt{214}}{2*2}=\frac{-52-4\sqrt{214}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+4\sqrt{214}}{2*2}=\frac{-52+4\sqrt{214}}{4}
$