4.5+8x(7-2x)=-27.5

Solution for 4.5+8x(7-2x)=-27.5 equation:

4.5+8x(7-2x)=-27.5

We move all terms to the left:

4.5+8x(7-2x)-(-27.5)=0

We add all the numbers together, and all the variables

8x(-2x+7)+4.5-(-27.5)=0

We add all the numbers together, and all the variables

8x(-2x+7)+32=0

We multiply parentheses

-16x^2+56x+32=0

a = -16; b = 56; c = +32;
Δ = b2-4ac
Δ = 562-4·(-16)·32
Δ = 5184
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5184}=72$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(56)-72}{2*-16}=\frac{-128}{-32}
=+4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(56)+72}{2*-16}=\frac{16}{-32}
=-1/2
$