3400+450x=10x^2

Solution for 3400+450x=10x^2 equation:

3400+450x=10x^2

We move all terms to the left:

3400+450x-(10x^2)=0

determiningTheFunctionDomain
-10x^2+450x+3400=0

a = -10; b = 450; c = +3400;
Δ = b2-4ac
Δ = 4502-4·(-10)·3400
Δ = 338500
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:

$\sqrt{\Delta}=\sqrt{338500}=\sqrt{100*3385}=\sqrt{100}*\sqrt{3385}=10\sqrt{3385}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-10\sqrt{3385}}{2*-10}=\frac{-450-10\sqrt{3385}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+10\sqrt{3385}}{2*-10}=\frac{-450+10\sqrt{3385}}{-20}
$