7c^2-17=6C-15

Solution for 7c^2-17=6C-15 equation:

7c^2-17=6-15

We move all terms to the left:

7c^2-17-(6-15)=0

We add all the numbers together, and all the variables

7c^2-17-(-9)=0

We add all the numbers together, and all the variables

7c^2-8=0

a = 7; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·7·(-8)
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{14}}{2*7}=\frac{0-4\sqrt{14}}{14}
=-\frac{4\sqrt{14}}{14}
=-\frac{2\sqrt{14}}{7}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{14}}{2*7}=\frac{0+4\sqrt{14}}{14}
=\frac{4\sqrt{14}}{14}
=\frac{2\sqrt{14}}{7}
$