8x(7-3x)+1=4(2-x)(2+x)

Solution for 8x(7-3x)+1=4(2-x)(2+x) equation:

8x(7-3x)+1=4(2-x)(2+x)

We move all terms to the left:

8x(7-3x)+1-(4(2-x)(2+x))=0

We add all the numbers together, and all the variables

8x(-3x+7)-(4(-1x+2)(x+2))+1=0

We multiply parentheses

-24x^2+56x-(4(-1x+2)(x+2))+1=0

We multiply parentheses ..

-24x^2-(4(-1x^2-2x+2x+4))+56x+1=0


We calculate terms in parentheses: -(4(-1x^2-2x+2x+4)), so:

4(-1x^2-2x+2x+4)

We multiply parentheses

-4x^2-8x+8x+16

We add all the numbers together, and all the variables

-4x^2+16

Back to the equation:

-(-4x^2+16)


We get rid of parentheses

-24x^2+4x^2+56x-16+1=0

We add all the numbers together, and all the variables

-20x^2+56x-15=0

a = -20; b = 56; c = -15;
Δ = b2-4ac
Δ = 562-4·(-20)·(-15)
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{-(56)-44}{2*-20}=\frac{-100}{-40}
=2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+44}{2*-20}=\frac{-12}{-40}
=3/10
$