(-5+5r+5r^2)=(-2-8r^2-7r)

Solution for (-5+5r+5r^2)=(-2-8r^2-7r) equation:

(-5+5r+5r^2)=(-2-8r^2-7r)

We move all terms to the left:

(-5+5r+5r^2)-((-2-8r^2-7r))=0

We get rid of parentheses

5r^2-((-2-8r^2-7r))+5r-5=0


We calculate terms in parentheses: -((-2-8r^2-7r)), so:

(-2-8r^2-7r)

We get rid of parentheses

-8r^2-7r-2

Back to the equation:

-(-8r^2-7r-2)


We get rid of parentheses

5r^2+8r^2+7r+5r+2-5=0

We add all the numbers together, and all the variables

13r^2+12r-3=0

a = 13; b = 12; c = -3;
Δ = b2-4ac
Δ = 122-4·13·(-3)
Δ = 300
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:

$\sqrt{\Delta}=\sqrt{300}=\sqrt{100*3}=\sqrt{100}*\sqrt{3}=10\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-10\sqrt{3}}{2*13}=\frac{-12-10\sqrt{3}}{26}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+10\sqrt{3}}{2*13}=\frac{-12+10\sqrt{3}}{26}
$