5*35=x*4x

Solution for 5*35=x*4x equation:

5*35=x*4x

We move all terms to the left:

5*35-(x*4x)=0

We add all the numbers together, and all the variables

-(+x*4x)+5*35=0

We add all the numbers together, and all the variables

-(+x*4x)+175=0

We get rid of parentheses

-x*4x+175=0

Wy multiply elements

-4x^2+175=0

a = -4; b = 0; c = +175;
Δ = b2-4ac
Δ = 02-4·(-4)·175
Δ = 2800
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:

$\sqrt{\Delta}=\sqrt{2800}=\sqrt{400*7}=\sqrt{400}*\sqrt{7}=20\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{7}}{2*-4}=\frac{0-20\sqrt{7}}{-8}
=-\frac{20\sqrt{7}}{-8}
=-\frac{5\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{7}}{2*-4}=\frac{0+20\sqrt{7}}{-8}
=\frac{20\sqrt{7}}{-8}
=\frac{5\sqrt{7}}{-2}
$