7-3/10x=x

Solution for 7-3/10x=x equation:

7-3/10x=x

We move all terms to the left:

7-3/10x-(x)=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-3/10x+7=0

We multiply all the terms by the denominator


-1x*10x+7*10x-3=0

Wy multiply elements

-10x^2+70x-3=0

a = -10; b = 70; c = -3;
Δ = b2-4ac
Δ = 702-4·(-10)·(-3)
Δ = 4780
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:

$\sqrt{\Delta}=\sqrt{4780}=\sqrt{4*1195}=\sqrt{4}*\sqrt{1195}=2\sqrt{1195}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-2\sqrt{1195}}{2*-10}=\frac{-70-2\sqrt{1195}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+2\sqrt{1195}}{2*-10}=\frac{-70+2\sqrt{1195}}{-20}
$