2a(9-10a)=18a-20a^

Solution for 2a(9-10a)=18a-20a^ equation:

2a(9-10a)=18a-20a^

We move all terms to the left:

2a(9-10a)-(18a-20a^)=0

We add all the numbers together, and all the variables

2a(-10a+9)-(18a-20a^)=0

We multiply parentheses

-20a^2+18a-(18a-20a^)=0

We get rid of parentheses

-20a^2+18a-18a+20a^=0

We add all the numbers together, and all the variables

-20a^2+20a=0

a = -20; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-20)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-20}=\frac{-40}{-40}
=1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-20}=\frac{0}{-40}
=0
$