4x+5/2x+11=4

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

4x+5/2x+11=4

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x+5/2x+7=0

We multiply all the terms by the denominator


4x*2x+7*2x+5=0

Wy multiply elements

8x^2+14x+5=0

a = 8; b = 14; c = +5;
Δ = b2-4ac
Δ = 142-4·8·5
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6}{2*8}=\frac{-20}{16}
=-1+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6}{2*8}=\frac{-8}{16}
=-1/2
$