x^2=11x-12=0

Solution for x^2=11x-12=0 equation:

x^2=11x-12=0

We move all terms to the left:

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

We get rid of parentheses

x^2-11x+12=0

a = 1; b = -11; c = +12;
Δ = b2-4ac
Δ = -112-4·1·12
Δ = 73
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{73}}{2*1}=\frac{11-\sqrt{73}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{73}}{2*1}=\frac{11+\sqrt{73}}{2}
$