3(4x-8)=15x(35x+30)

Solution for 3(4x-8)=15x(35x+30) equation:

3(4x-8)=15x(35x+30)

We move all terms to the left:

3(4x-8)-(15x(35x+30))=0

We multiply parentheses

12x-(15x(35x+30))-24=0


We calculate terms in parentheses: -(15x(35x+30)), so:

15x(35x+30)

We multiply parentheses

525x^2+450x

Back to the equation:

-(525x^2+450x)


We get rid of parentheses

-525x^2+12x-450x-24=0

We add all the numbers together, and all the variables

-525x^2-438x-24=0

a = -525; b = -438; c = -24;
Δ = b2-4ac
Δ = -4382-4·(-525)·(-24)
Δ = 141444
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:

$\sqrt{\Delta}=\sqrt{141444}=\sqrt{36*3929}=\sqrt{36}*\sqrt{3929}=6\sqrt{3929}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-438)-6\sqrt{3929}}{2*-525}=\frac{438-6\sqrt{3929}}{-1050}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-438)+6\sqrt{3929}}{2*-525}=\frac{438+6\sqrt{3929}}{-1050}
$