7b^2=4b+24

Solution for 7b^2=4b+24 equation:

7b^2=4b+24

We move all terms to the left:

7b^2-(4b+24)=0

We get rid of parentheses

7b^2-4b-24=0

a = 7; b = -4; c = -24;
Δ = b2-4ac
Δ = -42-4·7·(-24)
Δ = 688
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{688}=\sqrt{16*43}=\sqrt{16}*\sqrt{43}=4\sqrt{43}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{43}}{2*7}=\frac{4-4\sqrt{43}}{14}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{43}}{2*7}=\frac{4+4\sqrt{43}}{14}
$