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

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

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

We move all terms to the left:

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

We multiply parentheses

6x^2+5x-54x-(5(x-6))=0


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

5(x-6)

We multiply parentheses

5x-30

Back to the equation:

-(5x-30)


We add all the numbers together, and all the variables

6x^2-49x-(5x-30)=0

We get rid of parentheses

6x^2-49x-5x+30=0

We add all the numbers together, and all the variables

6x^2-54x+30=0

a = 6; b = -54; c = +30;
Δ = b2-4ac
Δ = -542-4·6·30
Δ = 2196
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:

$\sqrt{\Delta}=\sqrt{2196}=\sqrt{36*61}=\sqrt{36}*\sqrt{61}=6\sqrt{61}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{61}}{2*6}=\frac{54-6\sqrt{61}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{61}}{2*6}=\frac{54+6\sqrt{61}}{12}
$