4(x+4)+2=2(x+9)2x

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

4(x+4)+2=2(x+9)2x

We move all terms to the left:

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

We multiply parentheses

4x-(2(x+9)2x)+16+2=0


We calculate terms in parentheses: -(2(x+9)2x), so:

2(x+9)2x

We multiply parentheses

4x^2+36x

Back to the equation:

-(4x^2+36x)


We add all the numbers together, and all the variables

4x-(4x^2+36x)+18=0

We get rid of parentheses

-4x^2+4x-36x+18=0

We add all the numbers together, and all the variables

-4x^2-32x+18=0

a = -4; b = -32; c = +18;
Δ = b2-4ac
Δ = -322-4·(-4)·18
Δ = 1312
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:

$\sqrt{\Delta}=\sqrt{1312}=\sqrt{16*82}=\sqrt{16}*\sqrt{82}=4\sqrt{82}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-4\sqrt{82}}{2*-4}=\frac{32-4\sqrt{82}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+4\sqrt{82}}{2*-4}=\frac{32+4\sqrt{82}}{-8}
$