4b(b+23)=8b+23

Solution for 4b(b+23)=8b+23 equation:

4b(b+23)=8b+23

We move all terms to the left:

4b(b+23)-(8b+23)=0

We multiply parentheses

4b^2+92b-(8b+23)=0

We get rid of parentheses

4b^2+92b-8b-23=0

We add all the numbers together, and all the variables

4b^2+84b-23=0

a = 4; b = 84; c = -23;
Δ = b2-4ac
Δ = 842-4·4·(-23)
Δ = 7424
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:

$\sqrt{\Delta}=\sqrt{7424}=\sqrt{256*29}=\sqrt{256}*\sqrt{29}=16\sqrt{29}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-16\sqrt{29}}{2*4}=\frac{-84-16\sqrt{29}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+16\sqrt{29}}{2*4}=\frac{-84+16\sqrt{29}}{8}
$