X-12/100*x=352

Solution for X-12/100*x=352 equation:

X-12/100X=352

We move all terms to the left:

X-12/100X-(352)=0


Domain of the equation: 100X!=0

X!=0/100

X!=0

X∈R


We multiply all the terms by the denominator


X*100X-352*100X-12=0

Wy multiply elements

100X^2-35200X-12=0

a = 100; b = -35200; c = -12;
Δ = b2-4ac
Δ = -352002-4·100·(-12)
Δ = 1239044800
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:

$\sqrt{\Delta}=\sqrt{1239044800}=\sqrt{1600*774403}=\sqrt{1600}*\sqrt{774403}=40\sqrt{774403}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35200)-40\sqrt{774403}}{2*100}=\frac{35200-40\sqrt{774403}}{200}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35200)+40\sqrt{774403}}{2*100}=\frac{35200+40\sqrt{774403}}{200}
$