6r^2+7r=5

Solution for 6r^2+7r=5 equation:

6r^2+7r=5

We move all terms to the left:

6r^2+7r-(5)=0

a = 6; b = 7; c = -5;
Δ = b2-4ac
Δ = 72-4·6·(-5)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-13}{2*6}=\frac{-20}{12}
=-1+2/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+13}{2*6}=\frac{6}{12}
=1/2
$