90=b1,5(b+2)+15+2b-9

Solution for 90=b1,5(b+2)+15+2b-9 equation:

90=b1.5(b+2)+15+2b-9

We move all terms to the left:

90-(b1.5(b+2)+15+2b-9)=0


We calculate terms in parentheses: -(b1.5(b+2)+15+2b-9), so:

b1.5(b+2)+15+2b-9

determiningTheFunctionDomain
b1.5(b+2)+2b+15-9

We add all the numbers together, and all the variables

2b+b1.5(b+2)+6

We multiply parentheses

b^2+2b+2b+6

We add all the numbers together, and all the variables

b^2+4b+6

Back to the equation:

-(b^2+4b+6)


We get rid of parentheses

-b^2-4b-6+90=0

We add all the numbers together, and all the variables

-1b^2-4b+84=0

a = -1; b = -4; c = +84;
Δ = b2-4ac
Δ = -42-4·(-1)·84
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{22}}{2*-1}=\frac{4-4\sqrt{22}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{22}}{2*-1}=\frac{4+4\sqrt{22}}{-2}
$