(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

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

(+10a^2-100a)-200a=0

We get rid of parentheses

10a^2-100a-200a=0

We add all the numbers together, and all the variables

10a^2-300a=0

a = 10; b = -300; c = 0;
Δ = b2-4ac
Δ = -3002-4·10·0
Δ = 90000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{90000}=300$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-300}{2*10}=\frac{0}{20}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+300}{2*10}=\frac{600}{20}
=30
$