3x-5/2x=25-5x

Solution for 3x-5/2x=25-5x equation:

3x-5/2x=25-5x

We move all terms to the left:

3x-5/2x-(25-5x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3x-5/2x-(-5x+25)=0

We get rid of parentheses

3x-5/2x+5x-25=0

We multiply all the terms by the denominator


3x*2x+5x*2x-25*2x-5=0

Wy multiply elements

6x^2+10x^2-50x-5=0

We add all the numbers together, and all the variables

16x^2-50x-5=0

a = 16; b = -50; c = -5;
Δ = b2-4ac
Δ = -502-4·16·(-5)
Δ = 2820
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:

$\sqrt{\Delta}=\sqrt{2820}=\sqrt{4*705}=\sqrt{4}*\sqrt{705}=2\sqrt{705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{705}}{2*16}=\frac{50-2\sqrt{705}}{32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{705}}{2*16}=\frac{50+2\sqrt{705}}{32}
$