1/5x*35=7x

Solution for 1/5x*35=7x equation:

1/5x*35=7x

We move all terms to the left:

1/5x*35-(7x)=0


Domain of the equation: 5x*35!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-7x+1/5x*35=0

We multiply all the terms by the denominator


-7x*5x*35+1=0

Wy multiply elements

-1225x^2*3+1=0

Wy multiply elements

-3675x^2+1=0

a = -3675; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-3675)·1
Δ = 14700
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:

$\sqrt{\Delta}=\sqrt{14700}=\sqrt{4900*3}=\sqrt{4900}*\sqrt{3}=70\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-70\sqrt{3}}{2*-3675}=\frac{0-70\sqrt{3}}{-7350}
=-\frac{70\sqrt{3}}{-7350}
=-\frac{\sqrt{3}}{-105}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+70\sqrt{3}}{2*-3675}=\frac{0+70\sqrt{3}}{-7350}
=\frac{70\sqrt{3}}{-7350}
=\frac{\sqrt{3}}{-105}
$