8a^2-5=10a

Solution for 8a^2-5=10a equation:

8a^2-5=10a

We move all terms to the left:

8a^2-5-(10a)=0

a = 8; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·8·(-5)
Δ = 260
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:

$\sqrt{\Delta}=\sqrt{260}=\sqrt{4*65}=\sqrt{4}*\sqrt{65}=2\sqrt{65}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{65}}{2*8}=\frac{10-2\sqrt{65}}{16}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{65}}{2*8}=\frac{10+2\sqrt{65}}{16}
$