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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

x2-(+38x)+9=0

We add all the numbers together, and all the variables

x^2-(+38x)+9=0

We get rid of parentheses

x^2-38x+9=0

a = 1; b = -38; c = +9;
Δ = b2-4ac
Δ = -382-4·1·9
Δ = 1408
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:

$\sqrt{\Delta}=\sqrt{1408}=\sqrt{64*22}=\sqrt{64}*\sqrt{22}=8\sqrt{22}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-38)-8\sqrt{22}}{2*1}=\frac{38-8\sqrt{22}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-38)+8\sqrt{22}}{2*1}=\frac{38+8\sqrt{22}}{2}
$