2x^2+6x-1.5=0

Solution for 2x^2+6x-1.5=0 equation:

2x^2+6x-1.5=0

a = 2; b = 6; c = -1.5;
Δ = b2-4ac
Δ = 62-4·2·(-1.5)
Δ = 48
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:

$\sqrt{\Delta}=\sqrt{48}=\sqrt{16*3}=\sqrt{16}*\sqrt{3}=4\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-4\sqrt{3}}{2*2}=\frac{-6-4\sqrt{3}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+4\sqrt{3}}{2*2}=\frac{-6+4\sqrt{3}}{4}
$