5=6b^2+7b

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

5=6b^2+7b

We move all terms to the left:

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

We get rid of parentheses

-6b^2-7b+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:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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