2*x^2=46*x+46

Solution for 2*x^2=46*x+46 equation:

2x^2=46x+46

We move all terms to the left:

2x^2-(46x+46)=0

We get rid of parentheses

2x^2-46x-46=0

a = 2; b = -46; c = -46;
Δ = b2-4ac
Δ = -462-4·2·(-46)
Δ = 2484
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:

$\sqrt{\Delta}=\sqrt{2484}=\sqrt{36*69}=\sqrt{36}*\sqrt{69}=6\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-6\sqrt{69}}{2*2}=\frac{46-6\sqrt{69}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+6\sqrt{69}}{2*2}=\frac{46+6\sqrt{69}}{4}
$