r^2-7r-15=-10r-r

Solution for r^2-7r-15=-10r-r equation:

r^2-7r-15=-10r-r

We move all terms to the left:

r^2-7r-15-(-10r-r)=0

We add all the numbers together, and all the variables

r^2-7r-(-11r)-15=0

We get rid of parentheses

r^2-7r+11r-15=0

We add all the numbers together, and all the variables

r^2+4r-15=0

a = 1; b = 4; c = -15;
Δ = b2-4ac
Δ = 42-4·1·(-15)
Δ = 76
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{19}}{2*1}=\frac{-4-2\sqrt{19}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{19}}{2*1}=\frac{-4+2\sqrt{19}}{2}
$