0=3x-5/2x+4

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

0=3x-5/2x+4

We move all terms to the left:

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


Domain of the equation: 2x+4)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

-6x^2-8x+5=0

a = -6; b = -8; c = +5;
Δ = b2-4ac
Δ = -82-4·(-6)·5
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{46}}{2*-6}=\frac{8-2\sqrt{46}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{46}}{2*-6}=\frac{8+2\sqrt{46}}{-12}
$