15c^2-16c+3=c^2

Solution for 15c^2-16c+3=c^2 equation:

15c^2-16c+3=c^2

We move all terms to the left:

15c^2-16c+3-(c^2)=0

determiningTheFunctionDomain
15c^2-c^2-16c+3=0

We add all the numbers together, and all the variables

14c^2-16c+3=0

a = 14; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·14·3
Δ = 88
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:

$\sqrt{\Delta}=\sqrt{88}=\sqrt{4*22}=\sqrt{4}*\sqrt{22}=2\sqrt{22}$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-2\sqrt{22}}{2*14}=\frac{16-2\sqrt{22}}{28}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+2\sqrt{22}}{2*14}=\frac{16+2\sqrt{22}}{28}
$