(1/8)(8x+15)=24

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Solution for (1/8)(8x+15)=24 equation:



(1/8)(8x+15)=24
We move all terms to the left:
(1/8)(8x+15)-(24)=0
Domain of the equation: 8)(8x+15)!=0
x∈R
We add all the numbers together, and all the variables
(+1/8)(8x+15)-24=0
We multiply parentheses ..
(+8x^2+1/8*15)-24=0
We multiply all the terms by the denominator
(+8x^2+1-24*8*15)=0
We get rid of parentheses
8x^2+1-24*8*15=0
We add all the numbers together, and all the variables
8x^2-2879=0
a = 8; b = 0; c = -2879;
Δ = b2-4ac
Δ = 02-4·8·(-2879)
Δ = 92128
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{92128}=\sqrt{16*5758}=\sqrt{16}*\sqrt{5758}=4\sqrt{5758}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{5758}}{2*8}=\frac{0-4\sqrt{5758}}{16} =-\frac{4\sqrt{5758}}{16} =-\frac{\sqrt{5758}}{4} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{5758}}{2*8}=\frac{0+4\sqrt{5758}}{16} =\frac{4\sqrt{5758}}{16} =\frac{\sqrt{5758}}{4} $

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