6(2)+15(2)=c(2)

Solution for 6(2)+15(2)=c(2) equation:

6(2)+15(2)=c(2)

We move all terms to the left:

6(2)+15(2)-(c(2))=0

determiningTheFunctionDomain
-c2+62+152=0

We add all the numbers together, and all the variables

-1c^2+214=0

a = -1; b = 0; c = +214;
Δ = b2-4ac
Δ = 02-4·(-1)·214
Δ = 856
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:

$\sqrt{\Delta}=\sqrt{856}=\sqrt{4*214}=\sqrt{4}*\sqrt{214}=2\sqrt{214}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{214}}{2*-1}=\frac{0-2\sqrt{214}}{-2}
=-\frac{2\sqrt{214}}{-2}
=-\frac{\sqrt{214}}{-1}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{214}}{2*-1}=\frac{0+2\sqrt{214}}{-2}
=\frac{2\sqrt{214}}{-2}
=\frac{\sqrt{214}}{-1}
$