4x-1/2x=-70

Solution for 4x-1/2x=-70 equation:

4x-1/2x=-70

We move all terms to the left:

4x-1/2x-(-70)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

4x-1/2x+70=0

We multiply all the terms by the denominator


4x*2x+70*2x-1=0

Wy multiply elements

8x^2+140x-1=0

a = 8; b = 140; c = -1;
Δ = b2-4ac
Δ = 1402-4·8·(-1)
Δ = 19632
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:

$\sqrt{\Delta}=\sqrt{19632}=\sqrt{16*1227}=\sqrt{16}*\sqrt{1227}=4\sqrt{1227}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-4\sqrt{1227}}{2*8}=\frac{-140-4\sqrt{1227}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+4\sqrt{1227}}{2*8}=\frac{-140+4\sqrt{1227}}{16}
$