-5x-7=1/2x+4

Solution for -5x-7=1/2x+4 equation:

-5x-7=1/2x+4

We move all terms to the left:

-5x-7-(1/2x+4)=0


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

x∈R


We get rid of parentheses

-5x-1/2x-4-7=0

We multiply all the terms by the denominator


-5x*2x-4*2x-7*2x-1=0

Wy multiply elements

-10x^2-8x-14x-1=0

We add all the numbers together, and all the variables

-10x^2-22x-1=0

a = -10; b = -22; c = -1;
Δ = b2-4ac
Δ = -222-4·(-10)·(-1)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{111}}{2*-10}=\frac{22-2\sqrt{111}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{111}}{2*-10}=\frac{22+2\sqrt{111}}{-20}
$