3/2x-15=4x-4

Solution for 3/2x-15=4x-4 equation:

3/2x-15=4x-4

We move all terms to the left:

3/2x-15-(4x-4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-4x+4-15=0

We multiply all the terms by the denominator


-4x*2x+4*2x-15*2x+3=0

Wy multiply elements

-8x^2+8x-30x+3=0

We add all the numbers together, and all the variables

-8x^2-22x+3=0

a = -8; b = -22; c = +3;
Δ = b2-4ac
Δ = -222-4·(-8)·3
Δ = 580
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:

$\sqrt{\Delta}=\sqrt{580}=\sqrt{4*145}=\sqrt{4}*\sqrt{145}=2\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{145}}{2*-8}=\frac{22-2\sqrt{145}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{145}}{2*-8}=\frac{22+2\sqrt{145}}{-16}
$