-5x(6x+20)+10=9(4x-2)

Solution for -5x(6x+20)+10=9(4x-2) equation:

-5x(6x+20)+10=9(4x-2)

We move all terms to the left:

-5x(6x+20)+10-(9(4x-2))=0

We multiply parentheses

-30x^2-100x-(9(4x-2))+10=0


We calculate terms in parentheses: -(9(4x-2)), so:

9(4x-2)

We multiply parentheses

36x-18

Back to the equation:

-(36x-18)


We get rid of parentheses

-30x^2-100x-36x+18+10=0

We add all the numbers together, and all the variables

-30x^2-136x+28=0

a = -30; b = -136; c = +28;
Δ = b2-4ac
Δ = -1362-4·(-30)·28
Δ = 21856
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{21856}=\sqrt{16*1366}=\sqrt{16}*\sqrt{1366}=4\sqrt{1366}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-136)-4\sqrt{1366}}{2*-30}=\frac{136-4\sqrt{1366}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-136)+4\sqrt{1366}}{2*-30}=\frac{136+4\sqrt{1366}}{-60}
$