x^2=11x+24

Solution for x^2=11x+24 equation:

x^2=11x+24

We move all terms to the left:

x^2-(11x+24)=0

We get rid of parentheses

x^2-11x-24=0

a = 1; b = -11; c = -24;
Δ = b2-4ac
Δ = -112-4·1·(-24)
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{-(-11)-\sqrt{217}}{2*1}=\frac{11-\sqrt{217}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{217}}{2*1}=\frac{11+\sqrt{217}}{2}
$