4r^2-28r=-24

Solution for 4r^2-28r=-24 equation:

4r^2-28r=-24

We move all terms to the left:

4r^2-28r-(-24)=0

We add all the numbers together, and all the variables

4r^2-28r+24=0

a = 4; b = -28; c = +24;
Δ = b2-4ac
Δ = -282-4·4·24
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-20}{2*4}=\frac{8}{8}
=1
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+20}{2*4}=\frac{48}{8}
=6
$