3x(50-x)=106

Solution for 3x(50-x)=106 equation:

3x(50-x)=106

We move all terms to the left:

3x(50-x)-(106)=0

We add all the numbers together, and all the variables

3x(-1x+50)-106=0

We multiply parentheses

-3x^2+150x-106=0

a = -3; b = 150; c = -106;
Δ = b2-4ac
Δ = 1502-4·(-3)·(-106)
Δ = 21228
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:

$\sqrt{\Delta}=\sqrt{21228}=\sqrt{4*5307}=\sqrt{4}*\sqrt{5307}=2\sqrt{5307}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(150)-2\sqrt{5307}}{2*-3}=\frac{-150-2\sqrt{5307}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(150)+2\sqrt{5307}}{2*-3}=\frac{-150+2\sqrt{5307}}{-6}
$