7+4x(x+8)=2(4x+5)+9

Solution for 7+4x(x+8)=2(4x+5)+9 equation:

7+4x(x+8)=2(4x+5)+9

We move all terms to the left:

7+4x(x+8)-(2(4x+5)+9)=0

We multiply parentheses

4x^2+32x-(2(4x+5)+9)+7=0


We calculate terms in parentheses: -(2(4x+5)+9), so:

2(4x+5)+9

We multiply parentheses

8x+10+9

We add all the numbers together, and all the variables

8x+19

Back to the equation:

-(8x+19)


We get rid of parentheses

4x^2+32x-8x-19+7=0

We add all the numbers together, and all the variables

4x^2+24x-12=0

a = 4; b = 24; c = -12;
Δ = b2-4ac
Δ = 242-4·4·(-12)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{3}}{2*4}=\frac{-24-16\sqrt{3}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{3}}{2*4}=\frac{-24+16\sqrt{3}}{8}
$