C=8s+3/2s+12

Solution for C=8s+3/2s+12 equation:

=8C+3/2C+12

We move all terms to the left:

-(8C+3/2C+12)=0


Domain of the equation: 2C+12)!=0

C∈R


We get rid of parentheses

-8C-3/2C-12=0

We multiply all the terms by the denominator


-8C*2C-12*2C-3=0

Wy multiply elements

-16C^2-24C-3=0

a = -16; b = -24; c = -3;
Δ = b2-4ac
Δ = -242-4·(-16)·(-3)
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$C_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-8\sqrt{6}}{2*-16}=\frac{24-8\sqrt{6}}{-32}
$
$C_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+8\sqrt{6}}{2*-16}=\frac{24+8\sqrt{6}}{-32}
$