-2x+6/1.5x=1

Solution for -2x+6/1.5x=1 equation:

-2x+6/1.5x=1

We move all terms to the left:

-2x+6/1.5x-(1)=0


Domain of the equation: 1.5x!=0

x!=0/1.5

x!=0

x∈R


We multiply all the terms by the denominator


-2x*1.5x-1*1.5x+6=0

Wy multiply elements

-2x^2-1x+6=0

a = -2; b = -1; c = +6;
Δ = b2-4ac
Δ = -12-4·(-2)·6
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*-2}=\frac{8}{-4}
=-2
$