100x*(100-37.5/100)=35

Solution for 100x*(100-37.5/100)=35 equation:

100x(100-37.5/100)=35

We move all terms to the left:

100x(100-37.5/100)-(35)=0

We add all the numbers together, and all the variables

100x(-37.5/100+100)-35=0

We multiply parentheses

-3700x^2+10000x-35=0

a = -3700; b = 10000; c = -35;
Δ = b2-4ac
Δ = 100002-4·(-3700)·(-35)
Δ = 99482000
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:

$\sqrt{\Delta}=\sqrt{99482000}=\sqrt{400*248705}=\sqrt{400}*\sqrt{248705}=20\sqrt{248705}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10000)-20\sqrt{248705}}{2*-3700}=\frac{-10000-20\sqrt{248705}}{-7400}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10000)+20\sqrt{248705}}{2*-3700}=\frac{-10000+20\sqrt{248705}}{-7400}
$