65x+15x^2=1000000

Solution for 65x+15x^2=1000000 equation:

65x+15x^2=1000000

We move all terms to the left:

65x+15x^2-(1000000)=0

a = 15; b = 65; c = -1000000;
Δ = b2-4ac
Δ = 652-4·15·(-1000000)
Δ = 60004225
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:

$\sqrt{\Delta}=\sqrt{60004225}=\sqrt{25*2400169}=\sqrt{25}*\sqrt{2400169}=5\sqrt{2400169}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(65)-5\sqrt{2400169}}{2*15}=\frac{-65-5\sqrt{2400169}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(65)+5\sqrt{2400169}}{2*15}=\frac{-65+5\sqrt{2400169}}{30}
$