(-1/2)(4x+2)=-5

Solution for (-1/2)(4x+2)=-5 equation:

(-1/2)(4x+2)=-5

We move all terms to the left:

(-1/2)(4x+2)-(-5)=0


Domain of the equation: 2)(4x+2)!=0

x∈R


We add all the numbers together, and all the variables

(-1/2)(4x+2)+5=0

We multiply parentheses ..

(-4x^2-1/2*2)+5=0

We multiply all the terms by the denominator


(-4x^2-1+5*2*2)=0

We get rid of parentheses

-4x^2-1+5*2*2=0

We add all the numbers together, and all the variables

-4x^2+19=0

a = -4; b = 0; c = +19;
Δ = b2-4ac
Δ = 02-4·(-4)·19
Δ = 304
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:

$\sqrt{\Delta}=\sqrt{304}=\sqrt{16*19}=\sqrt{16}*\sqrt{19}=4\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{19}}{2*-4}=\frac{0-4\sqrt{19}}{-8}
=-\frac{4\sqrt{19}}{-8}
=-\frac{\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{19}}{2*-4}=\frac{0+4\sqrt{19}}{-8}
=\frac{4\sqrt{19}}{-8}
=\frac{\sqrt{19}}{-2}
$