-5c+6=1/3c-26

Solution for -5c+6=1/3c-26 equation:

-5c+6=1/3c-26

We move all terms to the left:

-5c+6-(1/3c-26)=0


Domain of the equation: 3c-26)!=0

c∈R


We get rid of parentheses

-5c-1/3c+26+6=0

We multiply all the terms by the denominator


-5c*3c+26*3c+6*3c-1=0

Wy multiply elements

-15c^2+78c+18c-1=0

We add all the numbers together, and all the variables

-15c^2+96c-1=0

a = -15; b = 96; c = -1;
Δ = b2-4ac
Δ = 962-4·(-15)·(-1)
Δ = 9156
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:

$\sqrt{\Delta}=\sqrt{9156}=\sqrt{4*2289}=\sqrt{4}*\sqrt{2289}=2\sqrt{2289}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(96)-2\sqrt{2289}}{2*-15}=\frac{-96-2\sqrt{2289}}{-30}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(96)+2\sqrt{2289}}{2*-15}=\frac{-96+2\sqrt{2289}}{-30}
$