(x*x)+64=(x*x)+(x*x)+49

Solution for (x*x)+64=(x*x)+(x*x)+49 equation:

(x*x)+64=(x*x)+(x*x)+49

We move all terms to the left:

(x*x)+64-((x*x)+(x*x)+49)=0

We add all the numbers together, and all the variables

(+x*x)-((+x*x)+(+x*x)+49)+64=0

We get rid of parentheses

x*x-((+x*x)+(+x*x)+49)+64=0


We calculate terms in parentheses: -((+x*x)+(+x*x)+49), so:

(+x*x)+(+x*x)+49

We get rid of parentheses

x*x+x*x+49

Wy multiply elements

x^2+x^2+49

We add all the numbers together, and all the variables

2x^2+49

Back to the equation:

-(2x^2+49)


Wy multiply elements

x^2-(2x^2+49)+64=0

We get rid of parentheses

x^2-2x^2-49+64=0

We add all the numbers together, and all the variables

-1x^2+15=0

a = -1; b = 0; c = +15;
Δ = b2-4ac
Δ = 02-4·(-1)·15
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*-1}=\frac{0-2\sqrt{15}}{-2}
=-\frac{2\sqrt{15}}{-2}
=-\frac{\sqrt{15}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*-1}=\frac{0+2\sqrt{15}}{-2}
=\frac{2\sqrt{15}}{-2}
=\frac{\sqrt{15}}{-1}
$