(x+9)(x+9)+(x+7)(x+7)=34

Solution for (x+9)(x+9)+(x+7)(x+7)=34 equation:

(x+9)(x+9)+(x+7)(x+7)=34

We move all terms to the left:

(x+9)(x+9)+(x+7)(x+7)-(34)=0

We multiply parentheses ..

(+x^2+9x+9x+81)+(x+7)(x+7)-34=0

We get rid of parentheses

x^2+9x+9x+(x+7)(x+7)+81-34=0

We multiply parentheses ..

x^2+(+x^2+7x+7x+49)+9x+9x+81-34=0

We add all the numbers together, and all the variables

x^2+(+x^2+7x+7x+49)+18x+47=0

We get rid of parentheses

x^2+x^2+7x+7x+18x+49+47=0

We add all the numbers together, and all the variables

2x^2+32x+96=0

a = 2; b = 32; c = +96;
Δ = b2-4ac
Δ = 322-4·2·96
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-16}{2*2}=\frac{-48}{4}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+16}{2*2}=\frac{-16}{4}
=-4
$