x(14x+12x+100x)/1000=1000000

Solution for x(14x+12x+100x)/1000=1000000 equation:

x(14x+12x+100x)/1000=1000000

We move all terms to the left:

x(14x+12x+100x)/1000-(1000000)=0

We add all the numbers together, and all the variables

x(+126x)/1000-1000000=0

We multiply all the terms by the denominator


x(+126x)-1000000*1000=0

We add all the numbers together, and all the variables

x(+126x)-1000000000=0

We multiply parentheses

126x^2-1000000000=0

a = 126; b = 0; c = -1000000000;
Δ = b2-4ac
Δ = 02-4·126·(-1000000000)
Δ = 504000000000
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:

$\sqrt{\Delta}=\sqrt{504000000000}=\sqrt{14400000000*35}=\sqrt{14400000000}*\sqrt{35}=120000\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-120000\sqrt{35}}{2*126}=\frac{0-120000\sqrt{35}}{252}
=-\frac{120000\sqrt{35}}{252}
=-\frac{10000\sqrt{35}}{21}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+120000\sqrt{35}}{2*126}=\frac{0+120000\sqrt{35}}{252}
=\frac{120000\sqrt{35}}{252}
=\frac{10000\sqrt{35}}{21}
$