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

Solution for 0=(5x-8)(-x+3) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

-((5x-8)(-1x+3))+0=0

We add all the numbers together, and all the variables

-((5x-8)(-1x+3))=0

We multiply parentheses ..

-((-5x^2+15x+8x-24))=0


We calculate terms in parentheses: -((-5x^2+15x+8x-24)), so:

(-5x^2+15x+8x-24)

We get rid of parentheses

-5x^2+15x+8x-24

We add all the numbers together, and all the variables

-5x^2+23x-24

Back to the equation:

-(-5x^2+23x-24)


We get rid of parentheses

5x^2-23x+24=0

a = 5; b = -23; c = +24;
Δ = b2-4ac
Δ = -232-4·5·24
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-7}{2*5}=\frac{16}{10}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+7}{2*5}=\frac{30}{10}
=3
$