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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

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

We add all the numbers together, and all the variables

-6x^2-18x+3=0

a = -6; b = -18; c = +3;
Δ = b2-4ac
Δ = -182-4·(-6)·3
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{11}}{2*-6}=\frac{18-6\sqrt{11}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{11}}{2*-6}=\frac{18+6\sqrt{11}}{-12}
$