5c^2-35c=32

Solution for 5c^2-35c=32 equation:

5c^2-35c=32

We move all terms to the left:

5c^2-35c-(32)=0

a = 5; b = -35; c = -32;
Δ = b2-4ac
Δ = -352-4·5·(-32)
Δ = 1865
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{1865}}{2*5}=\frac{35-\sqrt{1865}}{10}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1865}}{2*5}=\frac{35+\sqrt{1865}}{10}
$