11x^2+7x=13

Solution for 11x^2+7x=13 equation:

11x^2+7x=13

We move all terms to the left:

11x^2+7x-(13)=0

a = 11; b = 7; c = -13;
Δ = b2-4ac
Δ = 72-4·11·(-13)
Δ = 621
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{621}=\sqrt{9*69}=\sqrt{9}*\sqrt{69}=3\sqrt{69}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{69}}{2*11}=\frac{-7-3\sqrt{69}}{22}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{69}}{2*11}=\frac{-7+3\sqrt{69}}{22}
$