6/15b-b=6

Solution for 6/15b-b=6 equation:

6/15b-b=6

We move all terms to the left:

6/15b-b-(6)=0


Domain of the equation: 15b!=0

b!=0/15

b!=0

b∈R


We add all the numbers together, and all the variables

-1b+6/15b-6=0

We multiply all the terms by the denominator


-1b*15b-6*15b+6=0

Wy multiply elements

-15b^2-90b+6=0

a = -15; b = -90; c = +6;
Δ = b2-4ac
Δ = -902-4·(-15)·6
Δ = 8460
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:

$\sqrt{\Delta}=\sqrt{8460}=\sqrt{36*235}=\sqrt{36}*\sqrt{235}=6\sqrt{235}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{235}}{2*-15}=\frac{90-6\sqrt{235}}{-30}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{235}}{2*-15}=\frac{90+6\sqrt{235}}{-30}
$