x^2+17-52=9x-4

Solution for x^2+17-52=9x-4 equation:

x^2+17-52=9x-4

We move all terms to the left:

x^2+17-52-(9x-4)=0

We add all the numbers together, and all the variables

x^2-(9x-4)-35=0

We get rid of parentheses

x^2-9x+4-35=0

We add all the numbers together, and all the variables

x^2-9x-31=0

a = 1; b = -9; c = -31;
Δ = b2-4ac
Δ = -92-4·1·(-31)
Δ = 205
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{-(-9)-\sqrt{205}}{2*1}=\frac{9-\sqrt{205}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{205}}{2*1}=\frac{9+\sqrt{205}}{2}
$