8x(X+2)=4(2x+9)

Solution for 8x(X+2)=4(2x+9) equation:

8x(x+2)=4(2x+9)

We move all terms to the left:

8x(x+2)-(4(2x+9))=0

We multiply parentheses

8x^2+16x-(4(2x+9))=0


We calculate terms in parentheses: -(4(2x+9)), so:

4(2x+9)

We multiply parentheses

8x+36

Back to the equation:

-(8x+36)


We get rid of parentheses

8x^2+16x-8x-36=0

We add all the numbers together, and all the variables

8x^2+8x-36=0

a = 8; b = 8; c = -36;
Δ = b2-4ac
Δ = 82-4·8·(-36)
Δ = 1216
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:

$\sqrt{\Delta}=\sqrt{1216}=\sqrt{64*19}=\sqrt{64}*\sqrt{19}=8\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{19}}{2*8}=\frac{-8-8\sqrt{19}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{19}}{2*8}=\frac{-8+8\sqrt{19}}{16}
$