6b^2-7b=24

Solution for 6b^2-7b=24 equation:

6b^2-7b=24

We move all terms to the left:

6b^2-7b-(24)=0

a = 6; b = -7; c = -24;
Δ = b2-4ac
Δ = -72-4·6·(-24)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-25}{2*6}=\frac{-18}{12}
=-1+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+25}{2*6}=\frac{32}{12}
=2+2/3
$