60x+10x^2=10000

Solution for 60x+10x^2=10000 equation:

60x+10x^2=10000

We move all terms to the left:

60x+10x^2-(10000)=0

a = 10; b = 60; c = -10000;
Δ = b2-4ac
Δ = 602-4·10·(-10000)
Δ = 403600
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:

$\sqrt{\Delta}=\sqrt{403600}=\sqrt{400*1009}=\sqrt{400}*\sqrt{1009}=20\sqrt{1009}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-20\sqrt{1009}}{2*10}=\frac{-60-20\sqrt{1009}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+20\sqrt{1009}}{2*10}=\frac{-60+20\sqrt{1009}}{20}
$