2x+46=2x^2+10

Solution for 2x+46=2x^2+10 equation:

2x+46=2x^2+10

We move all terms to the left:

2x+46-(2x^2+10)=0

We get rid of parentheses

-2x^2+2x-10+46=0

We add all the numbers together, and all the variables

-2x^2+2x+36=0

a = -2; b = 2; c = +36;
Δ = b2-4ac
Δ = 22-4·(-2)·36
Δ = 292
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:

$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{73}}{2*-2}=\frac{-2-2\sqrt{73}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{73}}{2*-2}=\frac{-2+2\sqrt{73}}{-4}
$