1.5x^2-x=4

Solution for 1.5x^2-x=4 equation:

1.5x^2-x=4

We move all terms to the left:

1.5x^2-x-(4)=0

We add all the numbers together, and all the variables

1.5x^2-1x-4=0

a = 1.5; b = -1; c = -4;
Δ = b2-4ac
Δ = -12-4·1.5·(-4)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5}{2*1.5}=\frac{-4}{3}
=-1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5}{2*1.5}=\frac{6}{3}
=2
$