0=(4x-2)(8x+10)

Solution for 0=(4x-2)(8x+10) equation:

0=(4x-2)(8x+10)

We move all terms to the left:

0-((4x-2)(8x+10))=0

We add all the numbers together, and all the variables

-((4x-2)(8x+10))=0

We multiply parentheses ..

-((+32x^2+40x-16x-20))=0


We calculate terms in parentheses: -((+32x^2+40x-16x-20)), so:

(+32x^2+40x-16x-20)

We get rid of parentheses

32x^2+40x-16x-20

We add all the numbers together, and all the variables

32x^2+24x-20

Back to the equation:

-(32x^2+24x-20)


We get rid of parentheses

-32x^2-24x+20=0

a = -32; b = -24; c = +20;
Δ = b2-4ac
Δ = -242-4·(-32)·20
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-56}{2*-32}=\frac{-32}{-64}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+56}{2*-32}=\frac{80}{-64}
=-1+1/4
$