14x(10-x)=42

Solution for 14x(10-x)=42 equation:

14x(10-x)=42

We move all terms to the left:

14x(10-x)-(42)=0

We add all the numbers together, and all the variables

14x(-1x+10)-42=0

We multiply parentheses

-14x^2+140x-42=0

a = -14; b = 140; c = -42;
Δ = b2-4ac
Δ = 1402-4·(-14)·(-42)
Δ = 17248
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:

$\sqrt{\Delta}=\sqrt{17248}=\sqrt{784*22}=\sqrt{784}*\sqrt{22}=28\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-28\sqrt{22}}{2*-14}=\frac{-140-28\sqrt{22}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+28\sqrt{22}}{2*-14}=\frac{-140+28\sqrt{22}}{-28}
$