-1/2x+4=-2x-3

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

-1/2x+4=-2x-3

We move all terms to the left:

-1/2x+4-(-2x-3)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x+2x+3+4=0

We multiply all the terms by the denominator


2x*2x+3*2x+4*2x-1=0

Wy multiply elements

4x^2+6x+8x-1=0

We add all the numbers together, and all the variables

4x^2+14x-1=0

a = 4; b = 14; c = -1;
Δ = b2-4ac
Δ = 142-4·4·(-1)
Δ = 212
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:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{53}}{2*4}=\frac{-14-2\sqrt{53}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{53}}{2*4}=\frac{-14+2\sqrt{53}}{8}
$