x-(25/100*x)=150

Solution for x-(25/100*x)=150 equation:

x-(25/100x)=150

We move all terms to the left:

x-(25/100x)-(150)=0


Domain of the equation: 100x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+25/100x)-150=0

We get rid of parentheses

x-25/100x-150=0

We multiply all the terms by the denominator


x*100x-150*100x-25=0

Wy multiply elements

100x^2-15000x-25=0

a = 100; b = -15000; c = -25;
Δ = b2-4ac
Δ = -150002-4·100·(-25)
Δ = 225010000
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:

$\sqrt{\Delta}=\sqrt{225010000}=\sqrt{10000*22501}=\sqrt{10000}*\sqrt{22501}=100\sqrt{22501}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15000)-100\sqrt{22501}}{2*100}=\frac{15000-100\sqrt{22501}}{200}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15000)+100\sqrt{22501}}{2*100}=\frac{15000+100\sqrt{22501}}{200}
$