6x-3x^2+5=0

Solution for 6x-3x^2+5=0 equation:

6x-3x^2+5=0

a = -3; b = 6; c = +5;
Δ = b2-4ac
Δ = 62-4·(-3)·5
Δ = 96
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:

$\sqrt{\Delta}=\sqrt{96}=\sqrt{16*6}=\sqrt{16}*\sqrt{6}=4\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{6}}{2*-3}=\frac{-6-4\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{6}}{2*-3}=\frac{-6+4\sqrt{6}}{-6}
$