(a-10)*(a+10)=200a=

Solution for (a-10)*(a+10)=200a= equation:

(a-10)(a+10)=200a=

We move all terms to the left:

(a-10)(a+10)-(200a)=0

We add all the numbers together, and all the variables

-200a+(a-10)(a+10)=0

We use the square of the difference formula

a^2-200a-100=0

a = 1; b = -200; c = -100;
Δ = b2-4ac
Δ = -2002-4·1·(-100)
Δ = 40400
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:

$\sqrt{\Delta}=\sqrt{40400}=\sqrt{400*101}=\sqrt{400}*\sqrt{101}=20\sqrt{101}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-20\sqrt{101}}{2*1}=\frac{200-20\sqrt{101}}{2}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+20\sqrt{101}}{2*1}=\frac{200+20\sqrt{101}}{2}
$