7x+11=x-3/2x=1

Solution for 7x+11=x-3/2x=1 equation:

7x+11=x-3/2x=1

We move all terms to the left:

7x+11-(x-3/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7x-(+x-3/2x)+11=0

We get rid of parentheses

7x-x+3/2x+11=0

We multiply all the terms by the denominator


7x*2x-x*2x+11*2x+3=0

Wy multiply elements

14x^2-2x^2+22x+3=0

We add all the numbers together, and all the variables

12x^2+22x+3=0

a = 12; b = 22; c = +3;
Δ = b2-4ac
Δ = 222-4·12·3
Δ = 340
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:

$\sqrt{\Delta}=\sqrt{340}=\sqrt{4*85}=\sqrt{4}*\sqrt{85}=2\sqrt{85}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(22)-2\sqrt{85}}{2*12}=\frac{-22-2\sqrt{85}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(22)+2\sqrt{85}}{2*12}=\frac{-22+2\sqrt{85}}{24}
$