2b(b-2)=5b+3

Solution for 2b(b-2)=5b+3 equation:

2b(b-2)=5b+3

We move all terms to the left:

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

We multiply parentheses

2b^2-4b-(5b+3)=0

We get rid of parentheses

2b^2-4b-5b-3=0

We add all the numbers together, and all the variables

2b^2-9b-3=0

a = 2; b = -9; c = -3;
Δ = b2-4ac
Δ = -92-4·2·(-3)
Δ = 105
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{-(-9)-\sqrt{105}}{2*2}=\frac{9-\sqrt{105}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{105}}{2*2}=\frac{9+\sqrt{105}}{4}
$