5x^2+30x=2000

Solution for 5x^2+30x=2000 equation:

5x^2+30x=2000

We move all terms to the left:

5x^2+30x-(2000)=0

a = 5; b = 30; c = -2000;
Δ = b2-4ac
Δ = 302-4·5·(-2000)
Δ = 40900
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:

$\sqrt{\Delta}=\sqrt{40900}=\sqrt{100*409}=\sqrt{100}*\sqrt{409}=10\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{409}}{2*5}=\frac{-30-10\sqrt{409}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{409}}{2*5}=\frac{-30+10\sqrt{409}}{10}
$