c(25+12c)=7

Solution for c(25+12c)=7 equation:

c(25+12c)=7

We move all terms to the left:

c(25+12c)-(7)=0

We add all the numbers together, and all the variables

c(12c+25)-7=0

We multiply parentheses

12c^2+25c-7=0

a = 12; b = 25; c = -7;
Δ = b2-4ac
Δ = 252-4·12·(-7)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-31}{2*12}=\frac{-56}{24}
=-2+1/3
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+31}{2*12}=\frac{6}{24}
=1/4
$