8n^2-36n=140

Solution for 8n^2-36n=140 equation:

8n^2-36n=140

We move all terms to the left:

8n^2-36n-(140)=0

a = 8; b = -36; c = -140;
Δ = b2-4ac
Δ = -362-4·8·(-140)
Δ = 5776
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5776}=76$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-76}{2*8}=\frac{-40}{16}
=-2+1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+76}{2*8}=\frac{112}{16}
=7
$