4=0.75x^2

Solution for 4=0.75x^2 equation:

4=0.75x^2

We move all terms to the left:

4-(0.75x^2)=0

We get rid of parentheses

-0.75x^2+4=0

a = -0.75; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-0.75)·4
Δ = 12
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:

$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{3}}{2*-0.75}=\frac{0-2\sqrt{3}}{-1.5}
=-\frac{2\sqrt{3}}{-1.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{3}}{2*-0.75}=\frac{0+2\sqrt{3}}{-1.5}
=\frac{2\sqrt{3}}{-1.5}
$