15x+3x2=6

Solution for 15x+3x2=6 equation:

15x+3x^2=6

We move all terms to the left:

15x+3x^2-(6)=0

a = 3; b = 15; c = -6;
Δ = b2-4ac
Δ = 152-4·3·(-6)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{33}}{2*3}=\frac{-15-3\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{33}}{2*3}=\frac{-15+3\sqrt{33}}{6}
$