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

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

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

We move all terms to the left:

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


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

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-10x+8x-4=0

We add all the numbers together, and all the variables

6x^2-2x-4=0

a = 6; b = -2; c = -4;
Δ = b2-4ac
Δ = -22-4·6·(-4)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-10}{2*6}=\frac{-8}{12}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+10}{2*6}=\frac{12}{12}
=1
$