x2+9x=52

Solution for x2+9x=52 equation:

x2+9x=52

We move all terms to the left:

x2+9x-(52)=0

We add all the numbers together, and all the variables

x^2+9x-52=0

a = 1; b = 9; c = -52;
Δ = b2-4ac
Δ = 92-4·1·(-52)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-17}{2*1}=\frac{-26}{2}
=-13
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+17}{2*1}=\frac{8}{2}
=4
$