4r^2-90=-2r

Solution for 4r^2-90=-2r equation:

4r^2-90=-2r

We move all terms to the left:

4r^2-90-(-2r)=0

We get rid of parentheses

4r^2+2r-90=0

a = 4; b = 2; c = -90;
Δ = b2-4ac
Δ = 22-4·4·(-90)
Δ = 1444
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1444}=38$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-38}{2*4}=\frac{-40}{8}
=-5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+38}{2*4}=\frac{36}{8}
=4+1/2
$