10(c+1)c=7

Solution for 10(c+1)c=7 equation:

10(c+1)c=7

We move all terms to the left:

10(c+1)c-(7)=0

We multiply parentheses

10c^2+10c-7=0

a = 10; b = 10; c = -7;
Δ = b2-4ac
Δ = 102-4·10·(-7)
Δ = 380
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{95}}{2*10}=\frac{-10-2\sqrt{95}}{20}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{95}}{2*10}=\frac{-10+2\sqrt{95}}{20}
$