384x+10000=400x^2

Solution for 384x+10000=400x^2 equation:

384x+10000=400x^2

We move all terms to the left:

384x+10000-(400x^2)=0

determiningTheFunctionDomain
-400x^2+384x+10000=0

a = -400; b = 384; c = +10000;
Δ = b2-4ac
Δ = 3842-4·(-400)·10000
Δ = 16147456
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:

$\sqrt{\Delta}=\sqrt{16147456}=\sqrt{1024*15769}=\sqrt{1024}*\sqrt{15769}=32\sqrt{15769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(384)-32\sqrt{15769}}{2*-400}=\frac{-384-32\sqrt{15769}}{-800}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(384)+32\sqrt{15769}}{2*-400}=\frac{-384+32\sqrt{15769}}{-800}
$