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

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

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

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

10x^2-25x+15x+2=0

We add all the numbers together, and all the variables

10x^2-10x+2=0

a = 10; b = -10; c = +2;
Δ = b2-4ac
Δ = -102-4·10·2
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{5}}{2*10}=\frac{10-2\sqrt{5}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{5}}{2*10}=\frac{10+2\sqrt{5}}{20}
$