7x^2+11x=-2

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

7x^2+11x=-2

We move all terms to the left:

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

We add all the numbers together, and all the variables

7x^2+11x+2=0

a = 7; b = 11; c = +2;
Δ = b2-4ac
Δ = 112-4·7·2
Δ = 65
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{65}}{2*7}=\frac{-11-\sqrt{65}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{65}}{2*7}=\frac{-11+\sqrt{65}}{14}
$