X^2-1.5x=2

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

X^2-1.5X=2

We move all terms to the left:

X^2-1.5X-(2)=0

a = 1; b = -1.5; c = -2;
Δ = b2-4ac
Δ = -1.52-4·1·(-2)
Δ = 10.25
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{10.25}}{2*1}=\frac{1.5-\sqrt{10.25}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1.5)+\sqrt{10.25}}{2*1}=\frac{1.5+\sqrt{10.25}}{2}
$