8x^2+5x=3000

Solution for 8x^2+5x=3000 equation:

8x^2+5x=3000

We move all terms to the left:

8x^2+5x-(3000)=0

a = 8; b = 5; c = -3000;
Δ = b2-4ac
Δ = 52-4·8·(-3000)
Δ = 96025
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:

$\sqrt{\Delta}=\sqrt{96025}=\sqrt{25*3841}=\sqrt{25}*\sqrt{3841}=5\sqrt{3841}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{3841}}{2*8}=\frac{-5-5\sqrt{3841}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{3841}}{2*8}=\frac{-5+5\sqrt{3841}}{16}
$