x=7;x2-52

Solution for x=7;x2-52 equation:

x=7x^2-52

We move all terms to the left:

x-(7x^2-52)=0

We get rid of parentheses

-7x^2+x+52=0

a = -7; b = 1; c = +52;
Δ = b2-4ac
Δ = 12-4·(-7)·52
Δ = 1457
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{1457}}{2*-7}=\frac{-1-\sqrt{1457}}{-14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{1457}}{2*-7}=\frac{-1+\sqrt{1457}}{-14}
$