3/2x-11+x=4x-1

Solution for 3/2x-11+x=4x-1 equation:

3/2x-11+x=4x-1

We move all terms to the left:

3/2x-11+x-(4x-1)=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-1)-11=0

We get rid of parentheses

x+3/2x-4x+1-11=0

We multiply all the terms by the denominator


x*2x-4x*2x+1*2x-11*2x+3=0

Wy multiply elements

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

We add all the numbers together, and all the variables

-6x^2-20x+3=0

a = -6; b = -20; c = +3;
Δ = b2-4ac
Δ = -202-4·(-6)·3
Δ = 472
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:

$\sqrt{\Delta}=\sqrt{472}=\sqrt{4*118}=\sqrt{4}*\sqrt{118}=2\sqrt{118}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{118}}{2*-6}=\frac{20-2\sqrt{118}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{118}}{2*-6}=\frac{20+2\sqrt{118}}{-12}
$