7/4x-x=5,1

Solution for 7/4x-x=5,1 equation:

7/4x-x=5.1

We move all terms to the left:

7/4x-x-(5.1)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+7/4x-5.1=0

We multiply all the terms by the denominator


-1x*4x-(5.1)*4x+7=0

We multiply parentheses

-1x*4x-20.4x+7=0

Wy multiply elements

-4x^2-20.4x+7=0

a = -4; b = -20.4; c = +7;
Δ = b2-4ac
Δ = -20.42-4·(-4)·7
Δ = 528.16
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{-(-20.4)-\sqrt{528.16}}{2*-4}=\frac{20.4-\sqrt{528.16}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20.4)+\sqrt{528.16}}{2*-4}=\frac{20.4+\sqrt{528.16}}{-8}
$