38b-b^2=357

Solution for 38b-b^2=357 equation:

38b-b^2=357

We move all terms to the left:

38b-b^2-(357)=0

We add all the numbers together, and all the variables

-1b^2+38b-357=0

a = -1; b = 38; c = -357;
Δ = b2-4ac
Δ = 382-4·(-1)·(-357)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-4}{2*-1}=\frac{-42}{-2}
=+21
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+4}{2*-1}=\frac{-34}{-2}
=+17
$