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

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

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

We move all terms to the left:

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

We multiply parentheses

9x-(3x(x+6))+90=0


We calculate terms in parentheses: -(3x(x+6)), so:

3x(x+6)

We multiply parentheses

3x^2+18x

Back to the equation:

-(3x^2+18x)


We get rid of parentheses

-3x^2+9x-18x+90=0

We add all the numbers together, and all the variables

-3x^2-9x+90=0

a = -3; b = -9; c = +90;
Δ = b2-4ac
Δ = -92-4·(-3)·90
Δ = 1161
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:

$\sqrt{\Delta}=\sqrt{1161}=\sqrt{9*129}=\sqrt{9}*\sqrt{129}=3\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{129}}{2*-3}=\frac{9-3\sqrt{129}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{129}}{2*-3}=\frac{9+3\sqrt{129}}{-6}
$