3x-2(x+6)=9x(x-10)

Solution for 3x-2(x+6)=9x(x-10) equation:

3x-2(x+6)=9x(x-10)

We move all terms to the left:

3x-2(x+6)-(9x(x-10))=0

We multiply parentheses

3x-2x-(9x(x-10))-12=0


We calculate terms in parentheses: -(9x(x-10)), so:

9x(x-10)

We multiply parentheses

9x^2-90x

Back to the equation:

-(9x^2-90x)


We add all the numbers together, and all the variables

x-(9x^2-90x)-12=0

We get rid of parentheses

-9x^2+x+90x-12=0

We add all the numbers together, and all the variables

-9x^2+91x-12=0

a = -9; b = 91; c = -12;
Δ = b2-4ac
Δ = 912-4·(-9)·(-12)
Δ = 7849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(91)-\sqrt{7849}}{2*-9}=\frac{-91-\sqrt{7849}}{-18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(91)+\sqrt{7849}}{2*-9}=\frac{-91+\sqrt{7849}}{-18}
$