4/x+3=2x+5

Solution for 4/x+3=2x+5 equation:

4/x+3=2x+5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


-2x*x-5*x+3*x+4=0

We add all the numbers together, and all the variables

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

Wy multiply elements

-2x^2-2x+4=0

a = -2; b = -2; c = +4;
Δ = b2-4ac
Δ = -22-4·(-2)·4
Δ = 36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{36}=6$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-6}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+6}{2*-2}=\frac{8}{-4}
=-2
$