0.75x=1.5-3x^2

Solution for 0.75x=1.5-3x^2 equation:

0.75x=1.5-3x^2

We move all terms to the left:

0.75x-(1.5-3x^2)=0

We get rid of parentheses

3x^2+0.75x-1.5=0

a = 3; b = 0.75; c = -1.5;
Δ = b2-4ac
Δ = 0.752-4·3·(-1.5)
Δ = 18.5625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0.75)-\sqrt{18.5625}}{2*3}=\frac{-0.75-\sqrt{18.5625}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0.75)+\sqrt{18.5625}}{2*3}=\frac{-0.75+\sqrt{18.5625}}{6}
$