(X-3)(x-3)+(x+5)(x+5)=81

Solution for (X-3)(x-3)+(x+5)(x+5)=81 equation:

(X-3)(X-3)+(X+5)(X+5)=81

We move all terms to the left:

(X-3)(X-3)+(X+5)(X+5)-(81)=0

We multiply parentheses ..

(+X^2-3X-3X+9)+(X+5)(X+5)-81=0

We get rid of parentheses

X^2-3X-3X+(X+5)(X+5)+9-81=0

We multiply parentheses ..

X^2+(+X^2+5X+5X+25)-3X-3X+9-81=0

We add all the numbers together, and all the variables

X^2+(+X^2+5X+5X+25)-6X-72=0

We get rid of parentheses

X^2+X^2+5X+5X-6X+25-72=0

We add all the numbers together, and all the variables

2X^2+4X-47=0

a = 2; b = 4; c = -47;
Δ = b2-4ac
Δ = 42-4·2·(-47)
Δ = 392
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:

$\sqrt{\Delta}=\sqrt{392}=\sqrt{196*2}=\sqrt{196}*\sqrt{2}=14\sqrt{2}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-14\sqrt{2}}{2*2}=\frac{-4-14\sqrt{2}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+14\sqrt{2}}{2*2}=\frac{-4+14\sqrt{2}}{4}
$