10/4x=x-1

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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} $

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