12x^2-11x=13

Solution for 12x^2-11x=13 equation:

12x^2-11x=13

We move all terms to the left:

12x^2-11x-(13)=0

a = 12; b = -11; c = -13;
Δ = b2-4ac
Δ = -112-4·12·(-13)
Δ = 745
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{745}}{2*12}=\frac{11-\sqrt{745}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{745}}{2*12}=\frac{11+\sqrt{745}}{24}
$