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

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

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

We move all terms to the left:

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


Domain of the equation: 2)x+1)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply all the terms by the denominator


-4x*2)x+1)-((+1=0

Wy multiply elements

-8x^2+1=0

a = -8; b = 0; c = +1;
Δ = b2-4ac
Δ = 02-4·(-8)·1
Δ = 32
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:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{2}}{2*-8}=\frac{0-4\sqrt{2}}{-16}
=-\frac{4\sqrt{2}}{-16}
=-\frac{\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{2}}{2*-8}=\frac{0+4\sqrt{2}}{-16}
=\frac{4\sqrt{2}}{-16}
=\frac{\sqrt{2}}{-4}
$