4(-5a-9)10a=-10a-4(11a-2)

Solution for 4(-5a-9)10a=-10a-4(11a-2) equation:

4(-5a-9)10a=-10a-4(11a-2)

We move all terms to the left:

4(-5a-9)10a-(-10a-4(11a-2))=0

We multiply parentheses

-200a^2-360a-(-10a-4(11a-2))=0


We calculate terms in parentheses: -(-10a-4(11a-2)), so:

-10a-4(11a-2)

We multiply parentheses

-10a-44a+8

We add all the numbers together, and all the variables

-54a+8

Back to the equation:

-(-54a+8)


We get rid of parentheses

-200a^2-360a+54a-8=0

We add all the numbers together, and all the variables

-200a^2-306a-8=0

a = -200; b = -306; c = -8;
Δ = b2-4ac
Δ = -3062-4·(-200)·(-8)
Δ = 87236
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:

$\sqrt{\Delta}=\sqrt{87236}=\sqrt{4*21809}=\sqrt{4}*\sqrt{21809}=2\sqrt{21809}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-306)-2\sqrt{21809}}{2*-200}=\frac{306-2\sqrt{21809}}{-400}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-306)+2\sqrt{21809}}{2*-200}=\frac{306+2\sqrt{21809}}{-400}
$