b+3/2b+4+45+26-90+90=540

Solution for b+3/2b+4+45+26-90+90=540 equation:

b+3/2b+4+45+26-90+90=540

We move all terms to the left:

b+3/2b+4+45+26-90+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-465=0

We multiply all the terms by the denominator


b*2b-465*2b+3=0

Wy multiply elements

2b^2-930b+3=0

a = 2; b = -930; c = +3;
Δ = b2-4ac
Δ = -9302-4·2·3
Δ = 864876
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:

$\sqrt{\Delta}=\sqrt{864876}=\sqrt{4*216219}=\sqrt{4}*\sqrt{216219}=2\sqrt{216219}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-930)-2\sqrt{216219}}{2*2}=\frac{930-2\sqrt{216219}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-930)+2\sqrt{216219}}{2*2}=\frac{930+2\sqrt{216219}}{4}
$