4x+7/2x=11

Solution for 4x+7/2x=11 equation:

4x+7/2x=11

We move all terms to the left:

4x+7/2x-(11)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


4x*2x-11*2x+7=0

Wy multiply elements

8x^2-22x+7=0

a = 8; b = -22; c = +7;
Δ = b2-4ac
Δ = -222-4·8·7
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{65}}{2*8}=\frac{22-2\sqrt{65}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{65}}{2*8}=\frac{22+2\sqrt{65}}{16}
$