(=4-0.5x)(120-20x)

Solution for (=4-0.5x)(120-20x) equation:

(=4-0.5x)(120-20x)

We move all terms to the left:

(-(4-0.5x)(120-20x))=0

We add all the numbers together, and all the variables

(-(-0.5x+4)(-20x+120))=0

We multiply parentheses ..

(-(+0x^2+0x-80x+480))=0


We calculate terms in parentheses: +(-(+0x^2+0x-80x+480)), so:

-(+0x^2+0x-80x+480)

We get rid of parentheses

-0x^2-0x+80x-480

We add all the numbers together, and all the variables

-1x^2+79x-480

Back to the equation:

+(-1x^2+79x-480)


We get rid of parentheses

-1x^2+79x-480=0

a = -1; b = 79; c = -480;
Δ = b2-4ac
Δ = 792-4·(-1)·(-480)
Δ = 4321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(79)-\sqrt{4321}}{2*-1}=\frac{-79-\sqrt{4321}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(79)+\sqrt{4321}}{2*-1}=\frac{-79+\sqrt{4321}}{-2}
$