15-42/b=b

Solution for 15-42/b=b equation:

15-42/b=b

We move all terms to the left:

15-42/b-(b)=0


Domain of the equation: b!=0

b∈R


We add all the numbers together, and all the variables

-1b-42/b+15=0

We multiply all the terms by the denominator


-1b*b+15*b-42=0

We add all the numbers together, and all the variables

15b-1b*b-42=0

Wy multiply elements

-1b^2+15b-42=0

a = -1; b = 15; c = -42;
Δ = b2-4ac
Δ = 152-4·(-1)·(-42)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-\sqrt{57}}{2*-1}=\frac{-15-\sqrt{57}}{-2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{57}}{2*-1}=\frac{-15+\sqrt{57}}{-2}
$