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

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

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

We move all terms to the left:

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

We multiply parentheses

36x^2+72x-(4x(6x-10))=0


We calculate terms in parentheses: -(4x(6x-10)), so:

4x(6x-10)

We multiply parentheses

24x^2-40x

Back to the equation:

-(24x^2-40x)


We get rid of parentheses

36x^2-24x^2+72x+40x=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{-224}{24}
=-9+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(112)+112}{2*12}=\frac{0}{24}
=0
$