2(2a-9)=2a-10a(a-1)

Solution for 2(2a-9)=2a-10a(a-1) equation:

2(2a-9)=2a-10a(a-1)

We move all terms to the left:

2(2a-9)-(2a-10a(a-1))=0

We multiply parentheses

4a-(2a-10a(a-1))-18=0


We calculate terms in parentheses: -(2a-10a(a-1)), so:

2a-10a(a-1)

We multiply parentheses

-10a^2+2a+10a

We add all the numbers together, and all the variables

-10a^2+12a

Back to the equation:

-(-10a^2+12a)


We get rid of parentheses

10a^2-12a+4a-18=0

We add all the numbers together, and all the variables

10a^2-8a-18=0

a = 10; b = -8; c = -18;
Δ = b2-4ac
Δ = -82-4·10·(-18)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-28}{2*10}=\frac{-20}{20}
=-1
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+28}{2*10}=\frac{36}{20}
=1+4/5
$