5x2-11x-89=-11

Solution for 5x2-11x-89=-11 equation:

5x^2-11x-89=-11

We move all terms to the left:

5x^2-11x-89-(-11)=0

We add all the numbers together, and all the variables

5x^2-11x-78=0

a = 5; b = -11; c = -78;
Δ = b2-4ac
Δ = -112-4·5·(-78)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-41}{2*5}=\frac{-30}{10}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+41}{2*5}=\frac{52}{10}
=5+1/5
$