5=x+3/2x-5

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

5=x+3/2x-5

We move all terms to the left:

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


Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-2x^2+10x+10x-3=0

We add all the numbers together, and all the variables

-2x^2+20x-3=0

a = -2; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·(-2)·(-3)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{94}}{2*-2}=\frac{-20-2\sqrt{94}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{94}}{2*-2}=\frac{-20+2\sqrt{94}}{-4}
$