2b-18=2/5b-3

Solution for 2b-18=2/5b-3 equation:

2b-18=2/5b-3

We move all terms to the left:

2b-18-(2/5b-3)=0


Domain of the equation: 5b-3)!=0

b∈R


We get rid of parentheses

2b-2/5b+3-18=0

We multiply all the terms by the denominator


2b*5b+3*5b-18*5b-2=0

Wy multiply elements

10b^2+15b-90b-2=0

We add all the numbers together, and all the variables

10b^2-75b-2=0

a = 10; b = -75; c = -2;
Δ = b2-4ac
Δ = -752-4·10·(-2)
Δ = 5705
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{-(-75)-\sqrt{5705}}{2*10}=\frac{75-\sqrt{5705}}{20}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+\sqrt{5705}}{2*10}=\frac{75+\sqrt{5705}}{20}
$