10a2-10a=16

Solution for 10a2-10a=16 equation:

10a^2-10a=16

We move all terms to the left:

10a^2-10a-(16)=0

a = 10; b = -10; c = -16;
Δ = b2-4ac
Δ = -102-4·10·(-16)
Δ = 740
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:

$\sqrt{\Delta}=\sqrt{740}=\sqrt{4*185}=\sqrt{4}*\sqrt{185}=2\sqrt{185}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{185}}{2*10}=\frac{10-2\sqrt{185}}{20}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{185}}{2*10}=\frac{10+2\sqrt{185}}{20}
$