1.5x^2+2x=32

Solution for 1.5x^2+2x=32 equation:

1.5x^2+2x=32

We move all terms to the left:

1.5x^2+2x-(32)=0

a = 1.5; b = 2; c = -32;
Δ = b2-4ac
Δ = 22-4·1.5·(-32)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-14}{2*1.5}=\frac{-16}{3}
=-5+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+14}{2*1.5}=\frac{12}{3}
=4
$