X(299x-5x)=3000

Solution for X(299x-5x)=3000 equation:

X(299X-5X)=3000

We move all terms to the left:

X(299X-5X)-(3000)=0

We add all the numbers together, and all the variables

X(+294X)-3000=0

We multiply parentheses

294X^2-3000=0

a = 294; b = 0; c = -3000;
Δ = b2-4ac
Δ = 02-4·294·(-3000)
Δ = 3528000
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:

$\sqrt{\Delta}=\sqrt{3528000}=\sqrt{705600*5}=\sqrt{705600}*\sqrt{5}=840\sqrt{5}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-840\sqrt{5}}{2*294}=\frac{0-840\sqrt{5}}{588}
=-\frac{840\sqrt{5}}{588}
=-\frac{10\sqrt{5}}{7}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+840\sqrt{5}}{2*294}=\frac{0+840\sqrt{5}}{588}
=\frac{840\sqrt{5}}{588}
=\frac{10\sqrt{5}}{7}
$