4x(8x-15)=5x(6x+4)

Solution for 4x(8x-15)=5x(6x+4) equation:

4x(8x-15)=5x(6x+4)

We move all terms to the left:

4x(8x-15)-(5x(6x+4))=0

We multiply parentheses

32x^2-60x-(5x(6x+4))=0


We calculate terms in parentheses: -(5x(6x+4)), so:

5x(6x+4)

We multiply parentheses

30x^2+20x

Back to the equation:

-(30x^2+20x)


We get rid of parentheses

32x^2-30x^2-60x-20x=0

We add all the numbers together, and all the variables

2x^2-80x=0

a = 2; b = -80; c = 0;
Δ = b2-4ac
Δ = -802-4·2·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-80)-80}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-80)+80}{2*2}=\frac{160}{4}
=40
$