30x(x-3)+15(x-3)(x+3)=x(20x+8)

Solution for 30x(x-3)+15(x-3)(x+3)=x(20x+8) equation:

30x(x-3)+15(x-3)(x+3)=x(20x+8)

We move all terms to the left:

30x(x-3)+15(x-3)(x+3)-(x(20x+8))=0

We use the square of the difference formula

x^2+30x(x-3)-(x(20x+8))-9=0

We multiply parentheses

x^2+30x^2-90x-(x(20x+8))-9=0


We calculate terms in parentheses: -(x(20x+8)), so:

x(20x+8)

We multiply parentheses

20x^2+8x

Back to the equation:

-(20x^2+8x)


We add all the numbers together, and all the variables

31x^2-90x-(20x^2+8x)-9=0

We get rid of parentheses

31x^2-20x^2-90x-8x-9=0

We add all the numbers together, and all the variables

11x^2-98x-9=0

a = 11; b = -98; c = -9;
Δ = b2-4ac
Δ = -982-4·11·(-9)
Δ = 10000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{10000}=100$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-98)-100}{2*11}=\frac{-2}{22}
=-1/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-98)+100}{2*11}=\frac{198}{22}
=9
$