(8-4x)(6-2x)=30

Solution for (8-4x)(6-2x)=30 equation:

(8-4x)(6-2x)=30

We move all terms to the left:

(8-4x)(6-2x)-(30)=0

We add all the numbers together, and all the variables

(-4x+8)(-2x+6)-30=0

We multiply parentheses ..

(+8x^2-24x-16x+48)-30=0

We get rid of parentheses

8x^2-24x-16x+48-30=0

We add all the numbers together, and all the variables

8x^2-40x+18=0

a = 8; b = -40; c = +18;
Δ = b2-4ac
Δ = -402-4·8·18
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-32}{2*8}=\frac{8}{16}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+32}{2*8}=\frac{72}{16}
=4+1/2
$