1.5x+1=3/2x-8

Solution for 1.5x+1=3/2x-8 equation:

1.5x+1=3/2x-8

We move all terms to the left:

1.5x+1-(3/2x-8)=0


Domain of the equation: 2x-8)!=0

x∈R


We get rid of parentheses

1.5x-3/2x+8+1=0

We multiply all the terms by the denominator


(1.5x)*2x+8*2x+1*2x-3=0

We add all the numbers together, and all the variables

(+1.5x)*2x+8*2x+1*2x-3=0

We multiply parentheses

2x^2+8*2x+1*2x-3=0

Wy multiply elements

2x^2+16x+2x-3=0

We add all the numbers together, and all the variables

2x^2+18x-3=0

a = 2; b = 18; c = -3;
Δ = b2-4ac
Δ = 182-4·2·(-3)
Δ = 348
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{87}}{2*2}=\frac{-18-2\sqrt{87}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{87}}{2*2}=\frac{-18+2\sqrt{87}}{4}
$