5x+11=5/2x-4

Solution for 5x+11=5/2x-4 equation:

5x+11=5/2x-4

We move all terms to the left:

5x+11-(5/2x-4)=0


Domain of the equation: 2x-4)!=0

x∈R


We get rid of parentheses

5x-5/2x+4+11=0

We multiply all the terms by the denominator


5x*2x+4*2x+11*2x-5=0

Wy multiply elements

10x^2+8x+22x-5=0

We add all the numbers together, and all the variables

10x^2+30x-5=0

a = 10; b = 30; c = -5;
Δ = b2-4ac
Δ = 302-4·10·(-5)
Δ = 1100
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:

$\sqrt{\Delta}=\sqrt{1100}=\sqrt{100*11}=\sqrt{100}*\sqrt{11}=10\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{11}}{2*10}=\frac{-30-10\sqrt{11}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{11}}{2*10}=\frac{-30+10\sqrt{11}}{20}
$