5*35=6x*10x

Solution for 5*35=6x*10x equation:

5*35=6x*10x

We move all terms to the left:

5*35-(6x*10x)=0

We add all the numbers together, and all the variables

-(+6x*10x)+5*35=0

We add all the numbers together, and all the variables

-(+6x*10x)+175=0

We get rid of parentheses

-6x*10x+175=0

Wy multiply elements

-60x^2+175=0

a = -60; b = 0; c = +175;
Δ = b2-4ac
Δ = 02-4·(-60)·175
Δ = 42000
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:

$\sqrt{\Delta}=\sqrt{42000}=\sqrt{400*105}=\sqrt{400}*\sqrt{105}=20\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{105}}{2*-60}=\frac{0-20\sqrt{105}}{-120}
=-\frac{20\sqrt{105}}{-120}
=-\frac{\sqrt{105}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{105}}{2*-60}=\frac{0+20\sqrt{105}}{-120}
=\frac{20\sqrt{105}}{-120}
=\frac{\sqrt{105}}{-6}
$