-5/2x-3=x+4

Solution for -5/2x-3=x+4 equation:

-5/2x-3=x+4

We move all terms to the left:

-5/2x-3-(x+4)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-5/2x-x-4-3=0

We multiply all the terms by the denominator


-x*2x-4*2x-3*2x-5=0

Wy multiply elements

-2x^2-8x-6x-5=0

We add all the numbers together, and all the variables

-2x^2-14x-5=0

a = -2; b = -14; c = -5;
Δ = b2-4ac
Δ = -142-4·(-2)·(-5)
Δ = 156
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:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{39}}{2*-2}=\frac{14-2\sqrt{39}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{39}}{2*-2}=\frac{14+2\sqrt{39}}{-4}
$