6x=-2x^2+3

Solution for 6x=-2x^2+3 equation:

6x=-2x^2+3

We move all terms to the left:

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

We get rid of parentheses

2x^2+6x-3=0

a = 2; b = 6; c = -3;
Δ = b2-4ac
Δ = 62-4·2·(-3)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{15}}{2*2}=\frac{-6-2\sqrt{15}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{15}}{2*2}=\frac{-6+2\sqrt{15}}{4}
$