.75x^2+1.5x=4

Solution for .75x^2+1.5x=4 equation:

.75x^2+1.5x=4

We move all terms to the left:

.75x^2+1.5x-(4)=0

a = .75; b = 1.5; c = -4;
Δ = b2-4ac
Δ = 1.52-4·.75·(-4)
Δ = 14.25
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{-(1.5)-\sqrt{14.25}}{2*.75}=\frac{-1.5-\sqrt{14.25}}{1.5}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1.5)+\sqrt{14.25}}{2*.75}=\frac{-1.5+\sqrt{14.25}}{1.5}
$