x^2=61+2x

Solution for x^2=61+2x equation:

x^2=61+2x

We move all terms to the left:

x^2-(61+2x)=0

We add all the numbers together, and all the variables

x^2-(2x+61)=0

We get rid of parentheses

x^2-2x-61=0

a = 1; b = -2; c = -61;
Δ = b2-4ac
Δ = -22-4·1·(-61)
Δ = 248
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:

$\sqrt{\Delta}=\sqrt{248}=\sqrt{4*62}=\sqrt{4}*\sqrt{62}=2\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{62}}{2*1}=\frac{2-2\sqrt{62}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{62}}{2*1}=\frac{2+2\sqrt{62}}{2}
$