0=(X-3)(2x-8)

Solution for 0=(X-3)(2x-8) equation:

0=(X-3)(2X-8)

We move all terms to the left:

0-((X-3)(2X-8))=0

We add all the numbers together, and all the variables

-((X-3)(2X-8))=0

We multiply parentheses ..

-((+2X^2-8X-6X+24))=0


We calculate terms in parentheses: -((+2X^2-8X-6X+24)), so:

(+2X^2-8X-6X+24)

We get rid of parentheses

2X^2-8X-6X+24

We add all the numbers together, and all the variables

2X^2-14X+24

Back to the equation:

-(2X^2-14X+24)


We get rid of parentheses

-2X^2+14X-24=0

a = -2; b = 14; c = -24;
Δ = b2-4ac
Δ = 142-4·(-2)·(-24)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2}{2*-2}=\frac{-16}{-4}
=+4
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2}{2*-2}=\frac{-12}{-4}
=+3
$