7b^2-27b=40

Solution for 7b^2-27b=40 equation:

7b^2-27b=40

We move all terms to the left:

7b^2-27b-(40)=0

a = 7; b = -27; c = -40;
Δ = b2-4ac
Δ = -272-4·7·(-40)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-43}{2*7}=\frac{-16}{14}
=-1+1/7
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+43}{2*7}=\frac{70}{14}
=5
$