3*(x2+6)+17=7*(x2-4)

Solution for 3*(x2+6)+17=7*(x2-4) equation:

3(x2+6)+17=7(x2-4)

We move all terms to the left:

3(x2+6)+17-(7(x2-4))=0

We add all the numbers together, and all the variables

3(+x^2+6)-(7(+x^2-4))+17=0

We multiply parentheses

3x^2-(7(+x^2-4))+18+17=0


We calculate terms in parentheses: -(7(+x^2-4)), so:

7(+x^2-4)

We multiply parentheses

7x^2-28

Back to the equation:

-(7x^2-28)


We add all the numbers together, and all the variables

3x^2-(7x^2-28)+35=0

We get rid of parentheses

3x^2-7x^2+28+35=0

We add all the numbers together, and all the variables

-4x^2+63=0

a = -4; b = 0; c = +63;
Δ = b2-4ac
Δ = 02-4·(-4)·63
Δ = 1008
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:

$\sqrt{\Delta}=\sqrt{1008}=\sqrt{144*7}=\sqrt{144}*\sqrt{7}=12\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{7}}{2*-4}=\frac{0-12\sqrt{7}}{-8}
=-\frac{12\sqrt{7}}{-8}
=-\frac{3\sqrt{7}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{7}}{2*-4}=\frac{0+12\sqrt{7}}{-8}
=\frac{12\sqrt{7}}{-8}
=\frac{3\sqrt{7}}{-2}
$