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

We get rid of parentheses

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

We add all the numbers together, and all the variables

16c^2-16c+3=0

a = 16; b = -16; c = +3;
Δ = b2-4ac
Δ = -162-4·16·3
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8}{2*16}=\frac{8}{32}
=1/4
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*16}=\frac{24}{32}
=3/4
$