8x+1/2(6x)=154

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Solution for 8x+1/2(6x)=154 equation: 



8x+1/2(6x)=154

We move all terms to the left:

8x+1/2(6x)-(154)=0



Domain of the equation: 26x!=0

x!=0/26

x!=0

x∈R



We multiply all the terms by the denominator


8x*26x-154*26x+1=0

Wy multiply elements

208x^2-4004x+1=0

a = 208; b = -4004; c = +1;
Δ = b2-4ac
Δ = -40042-4·208·1
Δ = 16031184
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:


$\sqrt{\Delta}=\sqrt{16031184}=\sqrt{16*1001949}=\sqrt{16}*\sqrt{1001949}=4\sqrt{1001949}$


$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4004)-4\sqrt{1001949}}{2*208}=\frac{4004-4\sqrt{1001949}}{416}
$


$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4004)+4\sqrt{1001949}}{2*208}=\frac{4004+4\sqrt{1001949}}{416}
$

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