B+3/2b+(b+45)+(2b-90)+90=720

Solution for B+3/2b+(b+45)+(2b-90)+90=720 equation:

+3/2B+(B+45)+(2B-90)+90=720

We move all terms to the left:

+3/2B+(B+45)+(2B-90)+90-(720)=0


Domain of the equation: 2B!=0

B!=0/2

B!=0

B∈R


We add all the numbers together, and all the variables

3/2B+(B+45)+(2B-90)-630=0

We get rid of parentheses

3/2B+B+2B+45-90-630=0

We multiply all the terms by the denominator


B*2B+2B*2B+45*2B-90*2B-630*2B+3=0

Wy multiply elements

2B^2+4B^2+90B-180B-1260B+3=0

We add all the numbers together, and all the variables

6B^2-1350B+3=0

a = 6; b = -1350; c = +3;
Δ = b2-4ac
Δ = -13502-4·6·3
Δ = 1822428
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:

$\sqrt{\Delta}=\sqrt{1822428}=\sqrt{36*50623}=\sqrt{36}*\sqrt{50623}=6\sqrt{50623}$
$B_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1350)-6\sqrt{50623}}{2*6}=\frac{1350-6\sqrt{50623}}{12}
$
$B_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1350)+6\sqrt{50623}}{2*6}=\frac{1350+6\sqrt{50623}}{12}
$