10(2x+4)9x=6(6x+1)

Solution for 10(2x+4)9x=6(6x+1) equation:

10(2x+4)9x=6(6x+1)

We move all terms to the left:

10(2x+4)9x-(6(6x+1))=0

We multiply parentheses

180x^2+360x-(6(6x+1))=0


We calculate terms in parentheses: -(6(6x+1)), so:

6(6x+1)

We multiply parentheses

36x+6

Back to the equation:

-(36x+6)


We get rid of parentheses

180x^2+360x-36x-6=0

We add all the numbers together, and all the variables

180x^2+324x-6=0

a = 180; b = 324; c = -6;
Δ = b2-4ac
Δ = 3242-4·180·(-6)
Δ = 109296
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:

$\sqrt{\Delta}=\sqrt{109296}=\sqrt{144*759}=\sqrt{144}*\sqrt{759}=12\sqrt{759}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(324)-12\sqrt{759}}{2*180}=\frac{-324-12\sqrt{759}}{360}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(324)+12\sqrt{759}}{2*180}=\frac{-324+12\sqrt{759}}{360}
$