x+7+x-3+9+9=2(x-3)(x-4)

Solution for x+7+x-3+9+9=2(x-3)(x-4) equation:

x+7+x-3+9+9=2(x-3)(x-4)

We move all terms to the left:

x+7+x-3+9+9-(2(x-3)(x-4))=0

We add all the numbers together, and all the variables

2x-(2(x-3)(x-4))+22=0

We multiply parentheses ..

-(2(+x^2-4x-3x+12))+2x+22=0


We calculate terms in parentheses: -(2(+x^2-4x-3x+12)), so:

2(+x^2-4x-3x+12)

We multiply parentheses

2x^2-8x-6x+24

We add all the numbers together, and all the variables

2x^2-14x+24

Back to the equation:

-(2x^2-14x+24)


We add all the numbers together, and all the variables

2x-(2x^2-14x+24)+22=0

We get rid of parentheses

-2x^2+2x+14x-24+22=0

We add all the numbers together, and all the variables

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

a = -2; b = 16; c = -2;
Δ = b2-4ac
Δ = 162-4·(-2)·(-2)
Δ = 240
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:

$\sqrt{\Delta}=\sqrt{240}=\sqrt{16*15}=\sqrt{16}*\sqrt{15}=4\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{15}}{2*-2}=\frac{-16-4\sqrt{15}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{15}}{2*-2}=\frac{-16+4\sqrt{15}}{-4}
$