7x^2+7x=91

Solution for 7x^2+7x=91 equation:

7x^2+7x=91

We move all terms to the left:

7x^2+7x-(91)=0

a = 7; b = 7; c = -91;
Δ = b2-4ac
Δ = 72-4·7·(-91)
Δ = 2597
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:

$\sqrt{\Delta}=\sqrt{2597}=\sqrt{49*53}=\sqrt{49}*\sqrt{53}=7\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7\sqrt{53}}{2*7}=\frac{-7-7\sqrt{53}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7\sqrt{53}}{2*7}=\frac{-7+7\sqrt{53}}{14}
$