3x+4/2x-5=0

Solution for 3x+4/2x-5=0 equation:

3x+4/2x-5=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-10x+4=0

a = 6; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·6·4
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2}{2*6}=\frac{8}{12}
=2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*6}=\frac{12}{12}
=1
$