(6r^2-7r-20)=0

Solution for (6r^2-7r-20)=0 equation:

(6r^2-7r-20)=0

We get rid of parentheses

6r^2-7r-20=0

a = 6; b = -7; c = -20;
Δ = b2-4ac
Δ = -72-4·6·(-20)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-23}{2*6}=\frac{-16}{12}
=-1+1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+23}{2*6}=\frac{30}{12}
=2+1/2
$