10x(-2x-9)=-3(25-4x)

Solution for 10x(-2x-9)=-3(25-4x) equation:

10x(-2x-9)=-3(25-4x)

We move all terms to the left:

10x(-2x-9)-(-3(25-4x))=0

We add all the numbers together, and all the variables

10x(-2x-9)-(-3(-4x+25))=0

We multiply parentheses

-20x^2-90x-(-3(-4x+25))=0


We calculate terms in parentheses: -(-3(-4x+25)), so:

-3(-4x+25)

We multiply parentheses

12x-75

Back to the equation:

-(12x-75)


We get rid of parentheses

-20x^2-90x-12x+75=0

We add all the numbers together, and all the variables

-20x^2-102x+75=0

a = -20; b = -102; c = +75;
Δ = b2-4ac
Δ = -1022-4·(-20)·75
Δ = 16404
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:

$\sqrt{\Delta}=\sqrt{16404}=\sqrt{4*4101}=\sqrt{4}*\sqrt{4101}=2\sqrt{4101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-2\sqrt{4101}}{2*-20}=\frac{102-2\sqrt{4101}}{-40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+2\sqrt{4101}}{2*-20}=\frac{102+2\sqrt{4101}}{-40}
$