5/4b+(b-15)=150

Solution for 5/4b+(b-15)=150 equation:

5/4b+(b-15)=150

We move all terms to the left:

5/4b+(b-15)-(150)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R


We get rid of parentheses

5/4b+b-15-150=0

We multiply all the terms by the denominator


b*4b-15*4b-150*4b+5=0

Wy multiply elements

4b^2-60b-600b+5=0

We add all the numbers together, and all the variables

4b^2-660b+5=0

a = 4; b = -660; c = +5;
Δ = b2-4ac
Δ = -6602-4·4·5
Δ = 435520
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:

$\sqrt{\Delta}=\sqrt{435520}=\sqrt{64*6805}=\sqrt{64}*\sqrt{6805}=8\sqrt{6805}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-660)-8\sqrt{6805}}{2*4}=\frac{660-8\sqrt{6805}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-660)+8\sqrt{6805}}{2*4}=\frac{660+8\sqrt{6805}}{8}
$