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 add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

-5x^2+68x-30=0

a = -5; b = 68; c = -30;
Δ = b2-4ac
Δ = 682-4·(-5)·(-30)
Δ = 4024
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:

$\sqrt{\Delta}=\sqrt{4024}=\sqrt{4*1006}=\sqrt{4}*\sqrt{1006}=2\sqrt{1006}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(68)-2\sqrt{1006}}{2*-5}=\frac{-68-2\sqrt{1006}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(68)+2\sqrt{1006}}{2*-5}=\frac{-68+2\sqrt{1006}}{-10}
$