-3/2x+9/2=2/5x-5

Solution for -3/2x+9/2=2/5x-5 equation:

-3/2x+9/2=2/5x-5

We move all terms to the left:

-3/2x+9/2-(2/5x-5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 5x-5)!=0

x∈R


We get rid of parentheses

-3/2x-2/5x+5+9/2=0

We calculate fractions


(-15x)/40x^2+(-16x)/40x^2+45x/40x^2+5=0

We multiply all the terms by the denominator


(-15x)+(-16x)+45x+5*40x^2=0

We add all the numbers together, and all the variables

45x+(-15x)+(-16x)+5*40x^2=0

Wy multiply elements

200x^2+45x+(-15x)+(-16x)=0

We get rid of parentheses

200x^2+45x-15x-16x=0

We add all the numbers together, and all the variables

200x^2+14x=0

a = 200; b = 14; c = 0;
Δ = b2-4ac
Δ = 142-4·200·0
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-14}{2*200}=\frac{-28}{400}
=-7/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+14}{2*200}=\frac{0}{400}
=0
$