12-1,2(x-5)=22-2x(x+4)

Solution for 12-1,2(x-5)=22-2x(x+4) equation:

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

We move all terms to the left:

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

We multiply parentheses

-1.2x-(22-2x(x+4))+6+12=0


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

22-2x(x+4)

determiningTheFunctionDomain
-2x(x+4)+22

We multiply parentheses

-2x^2-8x+22

Back to the equation:

-(-2x^2-8x+22)


We add all the numbers together, and all the variables

-(-2x^2-8x+22)-1.2x+18=0

We get rid of parentheses

2x^2+8x-1.2x-22+18=0

We add all the numbers together, and all the variables

2x^2+6.8x-4=0

a = 2; b = 6.8; c = -4;
Δ = b2-4ac
Δ = 6.82-4·2·(-4)
Δ = 78.24
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{-(6.8)-\sqrt{78.24}}{2*2}=\frac{-6.8-\sqrt{78.24}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6.8)+\sqrt{78.24}}{2*2}=\frac{-6.8+\sqrt{78.24}}{4}
$