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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

-4x-1/2x-5=0

We multiply all the terms by the denominator


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

Wy multiply elements

-8x^2-10x-1=0

a = -8; b = -10; c = -1;
Δ = b2-4ac
Δ = -102-4·(-8)·(-1)
Δ = 68
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:

$\sqrt{\Delta}=\sqrt{68}=\sqrt{4*17}=\sqrt{4}*\sqrt{17}=2\sqrt{17}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{17}}{2*-8}=\frac{10-2\sqrt{17}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{17}}{2*-8}=\frac{10+2\sqrt{17}}{-16}
$