5x(14-x)=30-2x

Solution for 5x(14-x)=30-2x equation:

5x(14-x)=30-2x

We move all terms to the left:

5x(14-x)-(30-2x)=0

We add all the numbers together, and all the variables

5x(-1x+14)-(-2x+30)=0

We multiply parentheses

-5x^2+70x-(-2x+30)=0

We get rid of parentheses

-5x^2+70x+2x-30=0

We add all the numbers together, and all the variables

-5x^2+72x-30=0

a = -5; b = 72; c = -30;
Δ = b2-4ac
Δ = 722-4·(-5)·(-30)
Δ = 4584
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:

$\sqrt{\Delta}=\sqrt{4584}=\sqrt{4*1146}=\sqrt{4}*\sqrt{1146}=2\sqrt{1146}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-2\sqrt{1146}}{2*-5}=\frac{-72-2\sqrt{1146}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+2\sqrt{1146}}{2*-5}=\frac{-72+2\sqrt{1146}}{-10}
$