(-5x+15)/2x=x+1

Solution for (-5x+15)/2x=x+1 equation:

(-5x+15)/2x=x+1

We move all terms to the left:

(-5x+15)/2x-(x+1)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

(-5x+15)/2x-x-1=0

We multiply all the terms by the denominator


(-5x+15)-x*2x-1*2x=0

Wy multiply elements

-2x^2+(-5x+15)-2x=0

We get rid of parentheses

-2x^2-5x-2x+15=0

We add all the numbers together, and all the variables

-2x^2-7x+15=0

a = -2; b = -7; c = +15;
Δ = b2-4ac
Δ = -72-4·(-2)·15
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-13}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+13}{2*-2}=\frac{20}{-4}
=-5
$