-4r^2-7r-59=9-10r^2

Solution for -4r^2-7r-59=9-10r^2 equation:

-4r^2-7r-59=9-10r^2

We move all terms to the left:

-4r^2-7r-59-(9-10r^2)=0

We get rid of parentheses

-4r^2+10r^2-7r-9-59=0

We add all the numbers together, and all the variables

6r^2-7r-68=0

a = 6; b = -7; c = -68;
Δ = b2-4ac
Δ = -72-4·6·(-68)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-41}{2*6}=\frac{-34}{12}
=-2+5/6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+41}{2*6}=\frac{48}{12}
=4
$