7-5/2*8r-6+2r=32

Solution for 7-5/2*8r-6+2r=32 equation:

7-5/2*8r-6+2r=32

We move all terms to the left:

7-5/2*8r-6+2r-(32)=0


Domain of the equation: 2*8r!=0

r!=0/1

r!=0

r∈R


We add all the numbers together, and all the variables

2r-5/2*8r-31=0

We multiply all the terms by the denominator


2r*2*8r-31*2*8r-5=0

Wy multiply elements

32r^2*8-496r*8-5=0

Wy multiply elements

256r^2-3968r-5=0

a = 256; b = -3968; c = -5;
Δ = b2-4ac
Δ = -39682-4·256·(-5)
Δ = 15750144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{15750144}=\sqrt{9216*1709}=\sqrt{9216}*\sqrt{1709}=96\sqrt{1709}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3968)-96\sqrt{1709}}{2*256}=\frac{3968-96\sqrt{1709}}{512}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3968)+96\sqrt{1709}}{2*256}=\frac{3968+96\sqrt{1709}}{512}
$