4x(6x-10)=9x(4x+8)

Solution for 4x(6x-10)=9x(4x+8) equation:

4x(6x-10)=9x(4x+8)

We move all terms to the left:

4x(6x-10)-(9x(4x+8))=0

We multiply parentheses

24x^2-40x-(9x(4x+8))=0


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

9x(4x+8)

We multiply parentheses

36x^2+72x

Back to the equation:

-(36x^2+72x)


We get rid of parentheses

24x^2-36x^2-40x-72x=0

We add all the numbers together, and all the variables

-12x^2-112x=0

a = -12; b = -112; c = 0;
Δ = b2-4ac
Δ = -1122-4·(-12)·0
Δ = 12544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{12544}=112$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-112}{2*-12}=\frac{0}{-24}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+112}{2*-12}=\frac{224}{-24}
=-9+1/3
$