3(2)+7(2)=c(2)

Solution for 3(2)+7(2)=c(2) equation:

3(2)+7(2)=c(2)

We move all terms to the left:

3(2)+7(2)-(c(2))=0

determiningTheFunctionDomain
-c2+32+72=0

We add all the numbers together, and all the variables

-1c^2+104=0

a = -1; b = 0; c = +104;
Δ = b2-4ac
Δ = 02-4·(-1)·104
Δ = 416
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:

$\sqrt{\Delta}=\sqrt{416}=\sqrt{16*26}=\sqrt{16}*\sqrt{26}=4\sqrt{26}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{26}}{2*-1}=\frac{0-4\sqrt{26}}{-2}
=-\frac{4\sqrt{26}}{-2}
=-\frac{2\sqrt{26}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{26}}{2*-1}=\frac{0+4\sqrt{26}}{-2}
=\frac{4\sqrt{26}}{-2}
=\frac{2\sqrt{26}}{-1}
$