7/10x-X=1

Solution for 7/10x-X=1 equation:

7/10x-x=1

We move all terms to the left:

7/10x-x-(1)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/10x-1=0

We multiply all the terms by the denominator


-1x*10x-1*10x+7=0

Wy multiply elements

-10x^2-10x+7=0

a = -10; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·(-10)·7
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{95}}{2*-10}=\frac{10-2\sqrt{95}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{95}}{2*-10}=\frac{10+2\sqrt{95}}{-20}
$