3x(10x+4)=8(3x+6)

Solution for 3x(10x+4)=8(3x+6) equation:

3x(10x+4)=8(3x+6)

We move all terms to the left:

3x(10x+4)-(8(3x+6))=0

We multiply parentheses

30x^2+12x-(8(3x+6))=0


We calculate terms in parentheses: -(8(3x+6)), so:

8(3x+6)

We multiply parentheses

24x+48

Back to the equation:

-(24x+48)


We get rid of parentheses

30x^2+12x-24x-48=0

We add all the numbers together, and all the variables

30x^2-12x-48=0

a = 30; b = -12; c = -48;
Δ = b2-4ac
Δ = -122-4·30·(-48)
Δ = 5904
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:

$\sqrt{\Delta}=\sqrt{5904}=\sqrt{144*41}=\sqrt{144}*\sqrt{41}=12\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12\sqrt{41}}{2*30}=\frac{12-12\sqrt{41}}{60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12\sqrt{41}}{2*30}=\frac{12+12\sqrt{41}}{60}
$