1/2x+8=4x+3=16

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Solution for 1/2x+8=4x+3=16 equation:



1/2x+8=4x+3=16
We move all terms to the left:
1/2x+8-(4x+3)=0
Domain of the equation: 2x!=0
x!=0/2
x!=0
x∈R
We get rid of parentheses
1/2x-4x-3+8=0
We multiply all the terms by the denominator
-4x*2x-3*2x+8*2x+1=0
Wy multiply elements
-8x^2-6x+16x+1=0
We add all the numbers together, and all the variables
-8x^2+10x+1=0
a = -8; b = 10; c = +1;
Δ = b2-4ac
Δ = 102-4·(-8)·1
Δ = 132
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:
$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{33}}{2*-8}=\frac{-10-2\sqrt{33}}{-16} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{33}}{2*-8}=\frac{-10+2\sqrt{33}}{-16} $

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