1.3x-0.8x(x-5)=0.5(x-8)

Solution for 1.3x-0.8x(x-5)=0.5(x-8) equation:

1.3x-0.8x(x-5)=0.5(x-8)

We move all terms to the left:

1.3x-0.8x(x-5)-(0.5(x-8))=0

We multiply parentheses

-0x^2+1.3x-0x-(0.5(x-8))=0


We calculate terms in parentheses: -(0.5(x-8)), so:

0.5(x-8)

We multiply parentheses

0.5x-4

Back to the equation:

-(0.5x-4)


We add all the numbers together, and all the variables

-1x^2+0.3x-(0.5x-4)=0

We get rid of parentheses

-1x^2+0.3x-0.5x+4=0

We add all the numbers together, and all the variables

-1x^2-0.2x+4=0

a = -1; b = -0.2; c = +4;
Δ = b2-4ac
Δ = -0.22-4·(-1)·4
Δ = 16.04
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-0.2)-\sqrt{16.04}}{2*-1}=\frac{0.2-\sqrt{16.04}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.2)+\sqrt{16.04}}{2*-1}=\frac{0.2+\sqrt{16.04}}{-2}
$