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 = 236
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:

$\sqrt{\Delta}=\sqrt{236}=\sqrt{4*59}=\sqrt{4}*\sqrt{59}=2\sqrt{59}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{59}}{2*-2}=\frac{-14-2\sqrt{59}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{59}}{2*-2}=\frac{-14+2\sqrt{59}}{-4}
$