10/4x=x-1

Solution for 10/4x=x-1 equation:

10/4x=x-1

We move all terms to the left:

10/4x-(x-1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We get rid of parentheses

10/4x-x+1=0

We multiply all the terms by the denominator


-x*4x+1*4x+10=0

Wy multiply elements

-4x^2+4x+10=0

a = -4; b = 4; c = +10;
Δ = b2-4ac
Δ = 42-4·(-4)·10
Δ = 176
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:

$\sqrt{\Delta}=\sqrt{176}=\sqrt{16*11}=\sqrt{16}*\sqrt{11}=4\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{11}}{2*-4}=\frac{-4-4\sqrt{11}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{11}}{2*-4}=\frac{-4+4\sqrt{11}}{-8}
$