3x-8=10-3(x-4)x

Solution for 3x-8=10-3(x-4)x equation:

3x-8=10-3(x-4)x

We move all terms to the left:

3x-8-(10-3(x-4)x)=0


We calculate terms in parentheses: -(10-3(x-4)x), so:

10-3(x-4)x

determiningTheFunctionDomain
-3(x-4)x+10

We multiply parentheses

-3x^2+12x+10

Back to the equation:

-(-3x^2+12x+10)


We get rid of parentheses

3x^2-12x+3x-10-8=0

We add all the numbers together, and all the variables

3x^2-9x-18=0

a = 3; b = -9; c = -18;
Δ = b2-4ac
Δ = -92-4·3·(-18)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{33}}{2*3}=\frac{9-3\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{33}}{2*3}=\frac{9+3\sqrt{33}}{6}
$