15(x2-8)=8(x2+15)

Solution for 15(x2-8)=8(x2+15) equation:

15(x2-8)=8(x2+15)

We move all terms to the left:

15(x2-8)-(8(x2+15))=0

We add all the numbers together, and all the variables

15(+x^2-8)-(8(+x^2+15))=0

We multiply parentheses

15x^2-(8(+x^2+15))-120=0


We calculate terms in parentheses: -(8(+x^2+15)), so:

8(+x^2+15)

We multiply parentheses

8x^2+120

Back to the equation:

-(8x^2+120)


We get rid of parentheses

15x^2-8x^2-120-120=0

We add all the numbers together, and all the variables

7x^2-240=0

a = 7; b = 0; c = -240;
Δ = b2-4ac
Δ = 02-4·7·(-240)
Δ = 6720
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:

$\sqrt{\Delta}=\sqrt{6720}=\sqrt{64*105}=\sqrt{64}*\sqrt{105}=8\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{105}}{2*7}=\frac{0-8\sqrt{105}}{14}
=-\frac{8\sqrt{105}}{14}
=-\frac{4\sqrt{105}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{105}}{2*7}=\frac{0+8\sqrt{105}}{14}
=\frac{8\sqrt{105}}{14}
=\frac{4\sqrt{105}}{7}
$