7(2)+4(2)=c(2)

Solution for 7(2)+4(2)=c(2) equation:

7(2)+4(2)=c(2)

We move all terms to the left:

7(2)+4(2)-(c(2))=0

determiningTheFunctionDomain
-c2+72+42=0

We add all the numbers together, and all the variables

-1c^2+114=0

a = -1; b = 0; c = +114;
Δ = b2-4ac
Δ = 02-4·(-1)·114
Δ = 456
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:

$\sqrt{\Delta}=\sqrt{456}=\sqrt{4*114}=\sqrt{4}*\sqrt{114}=2\sqrt{114}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{114}}{2*-1}=\frac{0-2\sqrt{114}}{-2}
=-\frac{2\sqrt{114}}{-2}
=-\frac{\sqrt{114}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{114}}{2*-1}=\frac{0+2\sqrt{114}}{-2}
=\frac{2\sqrt{114}}{-2}
=\frac{\sqrt{114}}{-1}
$