6x2=11x+121

Solution for 6x2=11x+121 equation:

6x^2=11x+121

We move all terms to the left:

6x^2-(11x+121)=0

We get rid of parentheses

6x^2-11x-121=0

a = 6; b = -11; c = -121;
Δ = b2-4ac
Δ = -112-4·6·(-121)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-55}{2*6}=\frac{-44}{12}
=-3+2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+55}{2*6}=\frac{66}{12}
=5+1/2
$