4/5x-1=-3/2x+4

Solution for 4/5x-1=-3/2x+4 equation:

4/5x-1=-3/2x+4

We move all terms to the left:

4/5x-1-(-3/2x+4)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

4/5x+3/2x-4-1=0

We calculate fractions


8x/10x^2+15x/10x^2-4-1=0

We add all the numbers together, and all the variables

8x/10x^2+15x/10x^2-5=0

We multiply all the terms by the denominator


8x+15x-5*10x^2=0

We add all the numbers together, and all the variables

23x-5*10x^2=0

Wy multiply elements

-50x^2+23x=0

a = -50; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-50)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-50}=\frac{-46}{-100}
=23/50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-50}=\frac{0}{-100}
=0
$