(14-3c)7c=94

Solution for (14-3c)7c=94 equation:

(14-3c)7c=94

We move all terms to the left:

(14-3c)7c-(94)=0

We add all the numbers together, and all the variables

(-3c+14)7c-94=0

We multiply parentheses

-21c^2+98c-94=0

a = -21; b = 98; c = -94;
Δ = b2-4ac
Δ = 982-4·(-21)·(-94)
Δ = 1708
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:

$\sqrt{\Delta}=\sqrt{1708}=\sqrt{4*427}=\sqrt{4}*\sqrt{427}=2\sqrt{427}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(98)-2\sqrt{427}}{2*-21}=\frac{-98-2\sqrt{427}}{-42}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(98)+2\sqrt{427}}{2*-21}=\frac{-98+2\sqrt{427}}{-42}
$