8b^2-13b+6=5b^2

Solution for 8b^2-13b+6=5b^2 equation:

8b^2-13b+6=5b^2

We move all terms to the left:

8b^2-13b+6-(5b^2)=0

determiningTheFunctionDomain
8b^2-5b^2-13b+6=0

We add all the numbers together, and all the variables

3b^2-13b+6=0

a = 3; b = -13; c = +6;
Δ = b2-4ac
Δ = -132-4·3·6
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{97}}{2*3}=\frac{13-\sqrt{97}}{6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{97}}{2*3}=\frac{13+\sqrt{97}}{6}
$