11x^2-23x-84=0

Solution for 11x^2-23x-84=0 equation:

11x^2-23x-84=0

a = 11; b = -23; c = -84;
Δ = b2-4ac
Δ = -232-4·11·(-84)
Δ = 4225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4225}=65$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-65}{2*11}=\frac{-42}{22}
=-1+10/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+65}{2*11}=\frac{88}{22}
=4
$