b+3/2b+(b+25)+(2b-90)+90=540

Solution for b+3/2b+(b+25)+(2b-90)+90=540 equation:

b+3/2b+(b+25)+(2b-90)+90=540

We move all terms to the left:

b+3/2b+(b+25)+(2b-90)+90-(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

b+3/2b+(b+25)+(2b-90)-450=0

We get rid of parentheses

b+3/2b+b+2b+25-90-450=0

We multiply all the terms by the denominator


b*2b+b*2b+2b*2b+25*2b-90*2b-450*2b+3=0

Wy multiply elements

2b^2+2b^2+4b^2+50b-180b-900b+3=0

We add all the numbers together, and all the variables

8b^2-1030b+3=0

a = 8; b = -1030; c = +3;
Δ = b2-4ac
Δ = -10302-4·8·3
Δ = 1060804
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:

$\sqrt{\Delta}=\sqrt{1060804}=\sqrt{4*265201}=\sqrt{4}*\sqrt{265201}=2\sqrt{265201}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1030)-2\sqrt{265201}}{2*8}=\frac{1030-2\sqrt{265201}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1030)+2\sqrt{265201}}{2*8}=\frac{1030+2\sqrt{265201}}{16}
$