X.2(x+3)=8-3(x-4)

Solution for X.2(x+3)=8-3(x-4) equation:

X.2(X+3)=8-3(X-4)

We move all terms to the left:

X.2(X+3)-(8-3(X-4))=0

We multiply parentheses

X^2+3X-(8-3(X-4))=0


We calculate terms in parentheses: -(8-3(X-4)), so:

8-3(X-4)

determiningTheFunctionDomain
-3(X-4)+8

We multiply parentheses

-3X+12+8

We add all the numbers together, and all the variables

-3X+20

Back to the equation:

-(-3X+20)


We get rid of parentheses

X^2+3X+3X-20=0

We add all the numbers together, and all the variables

X^2+6X-20=0

a = 1; b = 6; c = -20;
Δ = b2-4ac
Δ = 62-4·1·(-20)
Δ = 116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{29}}{2*1}=\frac{-6-2\sqrt{29}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{29}}{2*1}=\frac{-6+2\sqrt{29}}{2}
$