2/5x-x=7

Solution for 2/5x-x=7 equation:

2/5x-x=7

We move all terms to the left:

2/5x-x-(7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+2/5x-7=0

We multiply all the terms by the denominator


-1x*5x-7*5x+2=0

Wy multiply elements

-5x^2-35x+2=0

a = -5; b = -35; c = +2;
Δ = b2-4ac
Δ = -352-4·(-5)·2
Δ = 1265
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{-(-35)-\sqrt{1265}}{2*-5}=\frac{35-\sqrt{1265}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1265}}{2*-5}=\frac{35+\sqrt{1265}}{-10}
$