X^2-52=5+4x

Solution for X^2-52=5+4x equation:

X^2-52=5+4X

We move all terms to the left:

X^2-52-(5+4X)=0

We add all the numbers together, and all the variables

X^2-(4X+5)-52=0

We get rid of parentheses

X^2-4X-5-52=0

We add all the numbers together, and all the variables

X^2-4X-57=0

a = 1; b = -4; c = -57;
Δ = b2-4ac
Δ = -42-4·1·(-57)
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{61}}{2*1}=\frac{4-2\sqrt{61}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{61}}{2*1}=\frac{4+2\sqrt{61}}{2}
$