X-80/100x=35

Solution for X-80/100x=35 equation:

X-80/100X=35

We move all terms to the left:

X-80/100X-(35)=0


Domain of the equation: 100X!=0

X!=0/100

X!=0

X∈R


We multiply all the terms by the denominator


X*100X-35*100X-80=0

Wy multiply elements

100X^2-3500X-80=0

a = 100; b = -3500; c = -80;
Δ = b2-4ac
Δ = -35002-4·100·(-80)
Δ = 12282000
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:

$\sqrt{\Delta}=\sqrt{12282000}=\sqrt{400*30705}=\sqrt{400}*\sqrt{30705}=20\sqrt{30705}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3500)-20\sqrt{30705}}{2*100}=\frac{3500-20\sqrt{30705}}{200}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3500)+20\sqrt{30705}}{2*100}=\frac{3500+20\sqrt{30705}}{200}
$