1.5b(b+2)=15(2b-9)

Solution for 1.5b(b+2)=15(2b-9) equation:

1.5b(b+2)=15(2b-9)

We move all terms to the left:

1.5b(b+2)-(15(2b-9))=0

We multiply parentheses

b^2+2b-(15(2b-9))=0


We calculate terms in parentheses: -(15(2b-9)), so:

15(2b-9)

We multiply parentheses

30b-135

Back to the equation:

-(30b-135)


We get rid of parentheses

b^2+2b-30b+135=0

We add all the numbers together, and all the variables

b^2-28b+135=0

a = 1; b = -28; c = +135;
Δ = b2-4ac
Δ = -282-4·1·135
Δ = 244
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:

$\sqrt{\Delta}=\sqrt{244}=\sqrt{4*61}=\sqrt{4}*\sqrt{61}=2\sqrt{61}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{61}}{2*1}=\frac{28-2\sqrt{61}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{61}}{2*1}=\frac{28+2\sqrt{61}}{2}
$