4b=1/3b-15

Solution for 4b=1/3b-15 equation:

4b=1/3b-15

We move all terms to the left:

4b-(1/3b-15)=0


Domain of the equation: 3b-15)!=0

b∈R


We get rid of parentheses

4b-1/3b+15=0

We multiply all the terms by the denominator


4b*3b+15*3b-1=0

Wy multiply elements

12b^2+45b-1=0

a = 12; b = 45; c = -1;
Δ = b2-4ac
Δ = 452-4·12·(-1)
Δ = 2073
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{-(45)-\sqrt{2073}}{2*12}=\frac{-45-\sqrt{2073}}{24}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+\sqrt{2073}}{2*12}=\frac{-45+\sqrt{2073}}{24}
$