5/2x=11-3x

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

5/2x=11-3x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

5/2x+3x-11=0

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-22x+5=0

a = 6; b = -22; c = +5;
Δ = b2-4ac
Δ = -222-4·6·5
Δ = 364
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:

$\sqrt{\Delta}=\sqrt{364}=\sqrt{4*91}=\sqrt{4}*\sqrt{91}=2\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{91}}{2*6}=\frac{22-2\sqrt{91}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{91}}{2*6}=\frac{22+2\sqrt{91}}{12}
$