52=x^2-3x

Solution for 52=x^2-3x equation:

52=x^2-3x

We move all terms to the left:

52-(x^2-3x)=0

We get rid of parentheses

-x^2+3x+52=0

We add all the numbers together, and all the variables

-1x^2+3x+52=0

a = -1; b = 3; c = +52;
Δ = b2-4ac
Δ = 32-4·(-1)·52
Δ = 217
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{-(3)-\sqrt{217}}{2*-1}=\frac{-3-\sqrt{217}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{217}}{2*-1}=\frac{-3+\sqrt{217}}{-2}
$