x(4-2)+9=3(5-x)+3x

Solution for x(4-2)+9=3(5-x)+3x equation:

x(4-2)+9=3(5-x)+3x

We move all terms to the left:

x(4-2)+9-(3(5-x)+3x)=0

We add all the numbers together, and all the variables

x2-(3(-1x+5)+3x)+9=0

We add all the numbers together, and all the variables

x^2-(3(-1x+5)+3x)+9=0


We calculate terms in parentheses: -(3(-1x+5)+3x), so:

3(-1x+5)+3x

We add all the numbers together, and all the variables

3x+3(-1x+5)

We multiply parentheses

3x-3x+15

We add all the numbers together, and all the variables

15

Back to the equation:

-(15)


We add all the numbers together, and all the variables

x^2-6=0

a = 1; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·1·(-6)
Δ = 24
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*1}=\frac{0-2\sqrt{6}}{2}
=-\frac{2\sqrt{6}}{2}
=-\sqrt{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*1}=\frac{0+2\sqrt{6}}{2}
=\frac{2\sqrt{6}}{2}
=\sqrt{6}
$