x/8x+4=3x+7*

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Solution for x/8x+4=3x+7* equation:



x/8x+4=3x+7*
We move all terms to the left:
x/8x+4-(3x+7*)=0
Domain of the equation: 8x!=0
x!=0/8
x!=0
x∈R
We add all the numbers together, and all the variables
x/8x-(+3x)+4=0
We get rid of parentheses
x/8x-3x+4=0
We multiply all the terms by the denominator
x-3x*8x+4*8x=0
Wy multiply elements
-24x^2+x+32x=0
We add all the numbers together, and all the variables
-24x^2+33x=0
a = -24; b = 33; c = 0;
Δ = b2-4ac
Δ = 332-4·(-24)·0
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-33}{2*-24}=\frac{-66}{-48} =1+3/8 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+33}{2*-24}=\frac{0}{-48} =0 $

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