3/2b+4b-135=540

Solution for 3/2b+4b-135=540 equation:

3/2b+4b-135=540

We move all terms to the left:

3/2b+4b-135-(540)=0


Domain of the equation: 2b!=0

b!=0/2

b!=0

b∈R


We add all the numbers together, and all the variables

4b+3/2b-675=0

We multiply all the terms by the denominator


4b*2b-675*2b+3=0

Wy multiply elements

8b^2-1350b+3=0

a = 8; b = -1350; c = +3;
Δ = b2-4ac
Δ = -13502-4·8·3
Δ = 1822404
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1822404}=\sqrt{4*455601}=\sqrt{4}*\sqrt{455601}=2\sqrt{455601}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1350)-2\sqrt{455601}}{2*8}=\frac{1350-2\sqrt{455601}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1350)+2\sqrt{455601}}{2*8}=\frac{1350+2\sqrt{455601}}{16}
$