x-75/100.x=350

Solution for x-75/100.x=350 equation:

x-75/100.x=350

We move all terms to the left:

x-75/100.x-(350)=0


Domain of the equation: 100.x!=0

x!=0/100.

x!=0

x∈R


We multiply all the terms by the denominator


x*100.x-350*100.x-75=0

Wy multiply elements

100x^2-35000x-75=0

a = 100; b = -35000; c = -75;
Δ = b2-4ac
Δ = -350002-4·100·(-75)
Δ = 1225030000
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:

$\sqrt{\Delta}=\sqrt{1225030000}=\sqrt{10000*122503}=\sqrt{10000}*\sqrt{122503}=100\sqrt{122503}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35000)-100\sqrt{122503}}{2*100}=\frac{35000-100\sqrt{122503}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35000)+100\sqrt{122503}}{2*100}=\frac{35000+100\sqrt{122503}}{200}
$