21r^2-186r+139=-5

Solution for 21r^2-186r+139=-5 equation:

21r^2-186r+139=-5

We move all terms to the left:

21r^2-186r+139-(-5)=0

We add all the numbers together, and all the variables

21r^2-186r+144=0

a = 21; b = -186; c = +144;
Δ = b2-4ac
Δ = -1862-4·21·144
Δ = 22500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{22500}=150$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-186)-150}{2*21}=\frac{36}{42}
=6/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-186)+150}{2*21}=\frac{336}{42}
=8
$