3x^2-16x+15=3

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

3x^2-16x+15=3

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2-16x+12=0

a = 3; b = -16; c = +12;
Δ = b2-4ac
Δ = -162-4·3·12
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{7}}{2*3}=\frac{16-4\sqrt{7}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{7}}{2*3}=\frac{16+4\sqrt{7}}{6}
$