7b^2=40-27b

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

7b^2=40-27b

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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