a2-20a=92

Solution for a2-20a=92 equation:

a2-20a=92

We move all terms to the left:

a2-20a-(92)=0

We add all the numbers together, and all the variables

a^2-20a-92=0

a = 1; b = -20; c = -92;
Δ = b2-4ac
Δ = -202-4·1·(-92)
Δ = 768
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:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-16\sqrt{3}}{2*1}=\frac{20-16\sqrt{3}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+16\sqrt{3}}{2*1}=\frac{20+16\sqrt{3}}{2}
$