10r^2-6=-9r

Solution for 10r^2-6=-9r equation:

10r^2-6=-9r

We move all terms to the left:

10r^2-6-(-9r)=0

We get rid of parentheses

10r^2+9r-6=0

a = 10; b = 9; c = -6;
Δ = b2-4ac
Δ = 92-4·10·(-6)
Δ = 321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{321}}{2*10}=\frac{-9-\sqrt{321}}{20}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{321}}{2*10}=\frac{-9+\sqrt{321}}{20}
$