13c(38-c)=434

Solution for 13c(38-c)=434 equation:

13c(38-c)=434

We move all terms to the left:

13c(38-c)-(434)=0

We add all the numbers together, and all the variables

13c(-1c+38)-434=0

We multiply parentheses

-13c^2+494c-434=0

a = -13; b = 494; c = -434;
Δ = b2-4ac
Δ = 4942-4·(-13)·(-434)
Δ = 221468
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:

$\sqrt{\Delta}=\sqrt{221468}=\sqrt{4*55367}=\sqrt{4}*\sqrt{55367}=2\sqrt{55367}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(494)-2\sqrt{55367}}{2*-13}=\frac{-494-2\sqrt{55367}}{-26}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(494)+2\sqrt{55367}}{2*-13}=\frac{-494+2\sqrt{55367}}{-26}
$