5/2x-3=x+11

Solution for 5/2x-3=x+11 equation:

5/2x-3=x+11

We move all terms to the left:

5/2x-3-(x+11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

5/2x-x-11-3=0

We multiply all the terms by the denominator


-x*2x-11*2x-3*2x+5=0

Wy multiply elements

-2x^2-22x-6x+5=0

We add all the numbers together, and all the variables

-2x^2-28x+5=0

a = -2; b = -28; c = +5;
Δ = b2-4ac
Δ = -282-4·(-2)·5
Δ = 824
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:

$\sqrt{\Delta}=\sqrt{824}=\sqrt{4*206}=\sqrt{4}*\sqrt{206}=2\sqrt{206}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-28)-2\sqrt{206}}{2*-2}=\frac{28-2\sqrt{206}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-28)+2\sqrt{206}}{2*-2}=\frac{28+2\sqrt{206}}{-4}
$