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

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

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

We move all terms to the left:

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

We multiply parentheses

9x^2+90x-(3(x+6))=0


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

3(x+6)

We multiply parentheses

3x+18

Back to the equation:

-(3x+18)


We get rid of parentheses

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

We add all the numbers together, and all the variables

9x^2+87x-18=0

a = 9; b = 87; c = -18;
Δ = b2-4ac
Δ = 872-4·9·(-18)
Δ = 8217
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:

$\sqrt{\Delta}=\sqrt{8217}=\sqrt{9*913}=\sqrt{9}*\sqrt{913}=3\sqrt{913}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(87)-3\sqrt{913}}{2*9}=\frac{-87-3\sqrt{913}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(87)+3\sqrt{913}}{2*9}=\frac{-87+3\sqrt{913}}{18}
$