X-5/100x=115

Solution for X-5/100x=115 equation:

X-5/100X=115

We move all terms to the left:

X-5/100X-(115)=0


Domain of the equation: 100X!=0

X!=0/100

X!=0

X∈R


We multiply all the terms by the denominator


X*100X-115*100X-5=0

Wy multiply elements

100X^2-11500X-5=0

a = 100; b = -11500; c = -5;
Δ = b2-4ac
Δ = -115002-4·100·(-5)
Δ = 132252000
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:

$\sqrt{\Delta}=\sqrt{132252000}=\sqrt{400*330630}=\sqrt{400}*\sqrt{330630}=20\sqrt{330630}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11500)-20\sqrt{330630}}{2*100}=\frac{11500-20\sqrt{330630}}{200}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11500)+20\sqrt{330630}}{2*100}=\frac{11500+20\sqrt{330630}}{200}
$