4r^2-21=25r

Solution for 4r^2-21=25r equation:

4r^2-21=25r

We move all terms to the left:

4r^2-21-(25r)=0

a = 4; b = -25; c = -21;
Δ = b2-4ac
Δ = -252-4·4·(-21)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-31}{2*4}=\frac{-6}{8}
=-3/4
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+31}{2*4}=\frac{56}{8}
=7
$