9x-12=3(x+5)6x

Solution for 9x-12=3(x+5)6x equation:

9x-12=3(x+5)6x

We move all terms to the left:

9x-12-(3(x+5)6x)=0


We calculate terms in parentheses: -(3(x+5)6x), so:

3(x+5)6x

We multiply parentheses

18x^2+90x

Back to the equation:

-(18x^2+90x)


We get rid of parentheses

-18x^2+9x-90x-12=0

We add all the numbers together, and all the variables

-18x^2-81x-12=0

a = -18; b = -81; c = -12;
Δ = b2-4ac
Δ = -812-4·(-18)·(-12)
Δ = 5697
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:

$\sqrt{\Delta}=\sqrt{5697}=\sqrt{9*633}=\sqrt{9}*\sqrt{633}=3\sqrt{633}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-81)-3\sqrt{633}}{2*-18}=\frac{81-3\sqrt{633}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+3\sqrt{633}}{2*-18}=\frac{81+3\sqrt{633}}{-36}
$