x-5/6x=1400

Solution for x-5/6x=1400 equation:

x-5/6x=1400

We move all terms to the left:

x-5/6x-(1400)=0


Domain of the equation: 6x!=0

x!=0/6

x!=0

x∈R


We multiply all the terms by the denominator


x*6x-1400*6x-5=0

Wy multiply elements

6x^2-8400x-5=0

a = 6; b = -8400; c = -5;
Δ = b2-4ac
Δ = -84002-4·6·(-5)
Δ = 70560120
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:

$\sqrt{\Delta}=\sqrt{70560120}=\sqrt{4*17640030}=\sqrt{4}*\sqrt{17640030}=2\sqrt{17640030}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8400)-2\sqrt{17640030}}{2*6}=\frac{8400-2\sqrt{17640030}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8400)+2\sqrt{17640030}}{2*6}=\frac{8400+2\sqrt{17640030}}{12}
$