1/2c*13=3c+48

Solution for 1/2c*13=3c+48 equation:

1/2c*13=3c+48

We move all terms to the left:

1/2c*13-(3c+48)=0


Domain of the equation: 2c*13!=0

c!=0/1

c!=0

c∈R


We get rid of parentheses

1/2c*13-3c-48=0

We multiply all the terms by the denominator


-3c*2c*13-48*2c*13+1=0

Wy multiply elements

-78c^2*1-1248c*1+1=0

Wy multiply elements

-78c^2-1248c+1=0

a = -78; b = -1248; c = +1;
Δ = b2-4ac
Δ = -12482-4·(-78)·1
Δ = 1557816
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:

$\sqrt{\Delta}=\sqrt{1557816}=\sqrt{4*389454}=\sqrt{4}*\sqrt{389454}=2\sqrt{389454}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1248)-2\sqrt{389454}}{2*-78}=\frac{1248-2\sqrt{389454}}{-156}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1248)+2\sqrt{389454}}{2*-78}=\frac{1248+2\sqrt{389454}}{-156}
$