2(1x)+1/2(8x)=4

Solution for 2(1x)+1/2(8x)=4 equation:

2(1x)+1/2(8x)=4

We move all terms to the left:

2(1x)+1/2(8x)-(4)=0


Domain of the equation: 28x!=0

x!=0/28

x!=0

x∈R


We multiply all the terms by the denominator


21x*28x-4*28x+1=0

Wy multiply elements

588x^2-112x+1=0

a = 588; b = -112; c = +1;
Δ = b2-4ac
Δ = -1122-4·588·1
Δ = 10192
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:

$\sqrt{\Delta}=\sqrt{10192}=\sqrt{784*13}=\sqrt{784}*\sqrt{13}=28\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-112)-28\sqrt{13}}{2*588}=\frac{112-28\sqrt{13}}{1176}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-112)+28\sqrt{13}}{2*588}=\frac{112+28\sqrt{13}}{1176}
$