x2-11x=152

Solution for x2-11x=152 equation:

x2-11x=152

We move all terms to the left:

x2-11x-(152)=0

We add all the numbers together, and all the variables

x^2-11x-152=0

a = 1; b = -11; c = -152;
Δ = b2-4ac
Δ = -112-4·1·(-152)
Δ = 729
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{729}=27$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-27}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+27}{2*1}=\frac{38}{2}
=19
$