30=0.5(x)(x-4)

Solution for 30=0.5(x)(x-4) equation:

30=0.5(x)(x-4)

We move all terms to the left:

30-(0.5(x)(x-4))=0


We calculate terms in parentheses: -(0.5x(x-4)), so:

0.5x(x-4)

We multiply parentheses

0x^2+0x

We add all the numbers together, and all the variables

x^2+x

Back to the equation:

-(x^2+x)


We get rid of parentheses

-x^2-x+30=0

We add all the numbers together, and all the variables

-1x^2-1x+30=0

a = -1; b = -1; c = +30;
Δ = b2-4ac
Δ = -12-4·(-1)·30
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-11}{2*-1}=\frac{-10}{-2}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+11}{2*-1}=\frac{12}{-2}
=-6
$