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

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

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

We move all terms to the left:

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

We multiply parentheses

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


We calculate terms in parentheses: -(5(3x-8)), so:

5(3x-8)

We multiply parentheses

15x-40

Back to the equation:

-(15x-40)


We get rid of parentheses

-4x^2+8x-15x+40=0

We add all the numbers together, and all the variables

-4x^2-7x+40=0

a = -4; b = -7; c = +40;
Δ = b2-4ac
Δ = -72-4·(-4)·40
Δ = 689
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{-(-7)-\sqrt{689}}{2*-4}=\frac{7-\sqrt{689}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{689}}{2*-4}=\frac{7+\sqrt{689}}{-8}
$