5b2=54+3b

Solution for 5b2=54+3b equation:

5b^2=54+3b

We move all terms to the left:

5b^2-(54+3b)=0

We add all the numbers together, and all the variables

5b^2-(3b+54)=0

We get rid of parentheses

5b^2-3b-54=0

a = 5; b = -3; c = -54;
Δ = b2-4ac
Δ = -32-4·5·(-54)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-33}{2*5}=\frac{-30}{10}
=-3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+33}{2*5}=\frac{36}{10}
=3+3/5
$