3/2x-11=4x-2

Solution for 3/2x-11=4x-2 equation:

3/2x-11=4x-2

We move all terms to the left:

3/2x-11-(4x-2)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

3/2x-4x+2-11=0

We multiply all the terms by the denominator


-4x*2x+2*2x-11*2x+3=0

Wy multiply elements

-8x^2+4x-22x+3=0

We add all the numbers together, and all the variables

-8x^2-18x+3=0

a = -8; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·(-8)·3
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{105}}{2*-8}=\frac{18-2\sqrt{105}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{105}}{2*-8}=\frac{18+2\sqrt{105}}{-16}
$