3x(5x-12)=8x-(4x-9)

Solution for 3x(5x-12)=8x-(4x-9) equation:

3x(5x-12)=8x-(4x-9)

We move all terms to the left:

3x(5x-12)-(8x-(4x-9))=0

We multiply parentheses

15x^2-36x-(8x-(4x-9))=0


We calculate terms in parentheses: -(8x-(4x-9)), so:

8x-(4x-9)

We get rid of parentheses

8x-4x+9

We add all the numbers together, and all the variables

4x+9

Back to the equation:

-(4x+9)


We get rid of parentheses

15x^2-36x-4x-9=0

We add all the numbers together, and all the variables

15x^2-40x-9=0

a = 15; b = -40; c = -9;
Δ = b2-4ac
Δ = -402-4·15·(-9)
Δ = 2140
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:

$\sqrt{\Delta}=\sqrt{2140}=\sqrt{4*535}=\sqrt{4}*\sqrt{535}=2\sqrt{535}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-2\sqrt{535}}{2*15}=\frac{40-2\sqrt{535}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+2\sqrt{535}}{2*15}=\frac{40+2\sqrt{535}}{30}
$