8x(2x-3)=5x(x+4)

Solution for 8x(2x-3)=5x(x+4) equation:

8x(2x-3)=5x(x+4)

We move all terms to the left:

8x(2x-3)-(5x(x+4))=0

We multiply parentheses

16x^2-24x-(5x(x+4))=0


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

5x(x+4)

We multiply parentheses

5x^2+20x

Back to the equation:

-(5x^2+20x)


We get rid of parentheses

16x^2-5x^2-24x-20x=0

We add all the numbers together, and all the variables

11x^2-44x=0

a = 11; b = -44; c = 0;
Δ = b2-4ac
Δ = -442-4·11·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-44}{2*11}=\frac{0}{22}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+44}{2*11}=\frac{88}{22}
=4
$