3x^2+5x=6000

Solution for 3x^2+5x=6000 equation:

3x^2+5x=6000

We move all terms to the left:

3x^2+5x-(6000)=0

a = 3; b = 5; c = -6000;
Δ = b2-4ac
Δ = 52-4·3·(-6000)
Δ = 72025
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:

$\sqrt{\Delta}=\sqrt{72025}=\sqrt{25*2881}=\sqrt{25}*\sqrt{2881}=5\sqrt{2881}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{2881}}{2*3}=\frac{-5-5\sqrt{2881}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{2881}}{2*3}=\frac{-5+5\sqrt{2881}}{6}
$