16a^2=7a^2+280a+1008

Solution for 16a^2=7a^2+280a+1008 equation:

16a^2=7a^2+280a+1008

We move all terms to the left:

16a^2-(7a^2+280a+1008)=0

We get rid of parentheses

16a^2-7a^2-280a-1008=0

We add all the numbers together, and all the variables

9a^2-280a-1008=0

a = 9; b = -280; c = -1008;
Δ = b2-4ac
Δ = -2802-4·9·(-1008)
Δ = 114688
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:

$\sqrt{\Delta}=\sqrt{114688}=\sqrt{16384*7}=\sqrt{16384}*\sqrt{7}=128\sqrt{7}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-280)-128\sqrt{7}}{2*9}=\frac{280-128\sqrt{7}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-280)+128\sqrt{7}}{2*9}=\frac{280+128\sqrt{7}}{18}
$