7x^2-15=-11x-5+x^2

Solution for 7x^2-15=-11x-5+x^2 equation:

7x^2-15=-11x-5+x^2

We move all terms to the left:

7x^2-15-(-11x-5+x^2)=0

We get rid of parentheses

7x^2-x^2+11x+5-15=0

We add all the numbers together, and all the variables

6x^2+11x-10=0

a = 6; b = 11; c = -10;
Δ = b2-4ac
Δ = 112-4·6·(-10)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-19}{2*6}=\frac{-30}{12}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+19}{2*6}=\frac{8}{12}
=2/3
$