35/4x+5*8=x

Solution for 35/4x+5*8=x equation:

35/4x+5*8=x

We move all terms to the left:

35/4x+5*8-(x)=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+35/4x+40=0

We multiply all the terms by the denominator


-1x*4x+40*4x+35=0

Wy multiply elements

-4x^2+160x+35=0

a = -4; b = 160; c = +35;
Δ = b2-4ac
Δ = 1602-4·(-4)·35
Δ = 26160
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:

$\sqrt{\Delta}=\sqrt{26160}=\sqrt{16*1635}=\sqrt{16}*\sqrt{1635}=4\sqrt{1635}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-4\sqrt{1635}}{2*-4}=\frac{-160-4\sqrt{1635}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+4\sqrt{1635}}{2*-4}=\frac{-160+4\sqrt{1635}}{-8}
$