12-1.2x(x-5)=22-2(x+4)

Solution for 12-1.2x(x-5)=22-2(x+4) equation:

12-1.2x(x-5)=22-2(x+4)

We move all terms to the left:

12-1.2x(x-5)-(22-2(x+4))=0

We multiply parentheses

-x^2+5x-(22-2(x+4))+12=0


We calculate terms in parentheses: -(22-2(x+4)), so:

22-2(x+4)

determiningTheFunctionDomain
-2(x+4)+22

We multiply parentheses

-2x-8+22

We add all the numbers together, and all the variables

-2x+14

Back to the equation:

-(-2x+14)


We add all the numbers together, and all the variables

-1x^2+5x-(-2x+14)+12=0

We get rid of parentheses

-1x^2+5x+2x-14+12=0

We add all the numbers together, and all the variables

-1x^2+7x-2=0

a = -1; b = 7; c = -2;
Δ = b2-4ac
Δ = 72-4·(-1)·(-2)
Δ = 41
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{-(7)-\sqrt{41}}{2*-1}=\frac{-7-\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{41}}{2*-1}=\frac{-7+\sqrt{41}}{-2}
$