2/5x+10=x-0.5

Solution for 2/5x+10=x-0.5 equation:

2/5x+10=x-0.5

We move all terms to the left:

2/5x+10-(x-0.5)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We get rid of parentheses

2/5x-x+0.5+10=0

We multiply all the terms by the denominator


-x*5x+(0.5)*5x+10*5x+2=0

We multiply parentheses

-x*5x+2.5x+10*5x+2=0

Wy multiply elements

-5x^2+2.5x+50x+2=0

We add all the numbers together, and all the variables

-5x^2+52.5x+2=0

a = -5; b = 52.5; c = +2;
Δ = b2-4ac
Δ = 52.52-4·(-5)·2
Δ = 2796.25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52.5)-\sqrt{2796.25}}{2*-5}=\frac{-52.5-\sqrt{2796.25}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52.5)+\sqrt{2796.25}}{2*-5}=\frac{-52.5+\sqrt{2796.25}}{-10}
$