2(x^2+34x-468)=0

Solution for 2(x^2+34x-468)=0 equation:

2(x^2+34x-468)=0

We multiply parentheses

2x^2+68x-936=0

a = 2; b = 68; c = -936;
Δ = b2-4ac
Δ = 682-4·2·(-936)
Δ = 12112
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:

$\sqrt{\Delta}=\sqrt{12112}=\sqrt{16*757}=\sqrt{16}*\sqrt{757}=4\sqrt{757}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-4\sqrt{757}}{2*2}=\frac{-68-4\sqrt{757}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+4\sqrt{757}}{2*2}=\frac{-68+4\sqrt{757}}{4}
$