2/5x-27=-5/2x+2

Solution for 2/5x-27=-5/2x+2 equation:

2/5x-27=-5/2x+2

We move all terms to the left:

2/5x-27-(-5/2x+2)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



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

x∈R


We get rid of parentheses

2/5x+5/2x-2-27=0

We calculate fractions


4x/10x^2+25x/10x^2-2-27=0

We add all the numbers together, and all the variables

4x/10x^2+25x/10x^2-29=0

We multiply all the terms by the denominator


4x+25x-29*10x^2=0

We add all the numbers together, and all the variables

29x-29*10x^2=0

Wy multiply elements

-290x^2+29x=0

a = -290; b = 29; c = 0;
Δ = b2-4ac
Δ = 292-4·(-290)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-29}{2*-290}=\frac{-58}{-580}
=1/10
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+29}{2*-290}=\frac{0}{-580}
=0
$