17/10x=4x

Solution for 17/10x=4x equation:

17/10x=4x

We move all terms to the left:

17/10x-(4x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

-4x+17/10x=0

We multiply all the terms by the denominator


-4x*10x+17=0

Wy multiply elements

-40x^2+17=0

a = -40; b = 0; c = +17;
Δ = b2-4ac
Δ = 02-4·(-40)·17
Δ = 2720
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:

$\sqrt{\Delta}=\sqrt{2720}=\sqrt{16*170}=\sqrt{16}*\sqrt{170}=4\sqrt{170}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{170}}{2*-40}=\frac{0-4\sqrt{170}}{-80}
=-\frac{4\sqrt{170}}{-80}
=-\frac{\sqrt{170}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{170}}{2*-40}=\frac{0+4\sqrt{170}}{-80}
=\frac{4\sqrt{170}}{-80}
=\frac{\sqrt{170}}{-20}
$