4r^2=36-7r

Solution for 4r^2=36-7r equation:

4r^2=36-7r

We move all terms to the left:

4r^2-(36-7r)=0

We add all the numbers together, and all the variables

4r^2-(-7r+36)=0

We get rid of parentheses

4r^2+7r-36=0

a = 4; b = 7; c = -36;
Δ = b2-4ac
Δ = 72-4·4·(-36)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-25}{2*4}=\frac{-32}{8}
=-4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+25}{2*4}=\frac{18}{8}
=2+1/4
$