3n^2+7n=1000

Solution for 3n^2+7n=1000 equation:

3n^2+7n=1000

We move all terms to the left:

3n^2+7n-(1000)=0

a = 3; b = 7; c = -1000;
Δ = b2-4ac
Δ = 72-4·3·(-1000)
Δ = 12049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{12049}}{2*3}=\frac{-7-\sqrt{12049}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{12049}}{2*3}=\frac{-7+\sqrt{12049}}{6}
$