2x+1/2x-3=-10

Solution for 2x+1/2x-3=-10 equation:

2x+1/2x-3=-10

We move all terms to the left:

2x+1/2x-3-(-10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

2x+1/2x+7=0

We multiply all the terms by the denominator


2x*2x+7*2x+1=0

Wy multiply elements

4x^2+14x+1=0

a = 4; b = 14; c = +1;
Δ = b2-4ac
Δ = 142-4·4·1
Δ = 180
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:

$\sqrt{\Delta}=\sqrt{180}=\sqrt{36*5}=\sqrt{36}*\sqrt{5}=6\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-6\sqrt{5}}{2*4}=\frac{-14-6\sqrt{5}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+6\sqrt{5}}{2*4}=\frac{-14+6\sqrt{5}}{8}
$