a(8a-a)=15

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Solution for a(8a-a)=15 equation:



a(8a-a)=15
We move all terms to the left:
a(8a-a)-(15)=0
We add all the numbers together, and all the variables
a(+7a)-15=0
We multiply parentheses
7a^2-15=0
a = 7; b = 0; c = -15;
Δ = b2-4ac
Δ = 02-4·7·(-15)
Δ = 420
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{105}}{2*7}=\frac{0-2\sqrt{105}}{14} =-\frac{2\sqrt{105}}{14} =-\frac{\sqrt{105}}{7} $
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{105}}{2*7}=\frac{0+2\sqrt{105}}{14} =\frac{2\sqrt{105}}{14} =\frac{\sqrt{105}}{7} $

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