5x+11=1/2x-3

Solution for 5x+11=1/2x-3 equation:

5x+11=1/2x-3

We move all terms to the left:

5x+11-(1/2x-3)=0


Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

5x-1/2x+3+11=0

We multiply all the terms by the denominator


5x*2x+3*2x+11*2x-1=0

Wy multiply elements

10x^2+6x+22x-1=0

We add all the numbers together, and all the variables

10x^2+28x-1=0

a = 10; b = 28; c = -1;
Δ = b2-4ac
Δ = 282-4·10·(-1)
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*10}=\frac{-28-2\sqrt{206}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+2\sqrt{206}}{2*10}=\frac{-28+2\sqrt{206}}{20}
$