X+5/2x-5=3

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

X+5/2X-5=3

We move all terms to the left:

X+5/2X-5-(3)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X+5/2X-8=0

We multiply all the terms by the denominator


X*2X-8*2X+5=0

Wy multiply elements

2X^2-16X+5=0

a = 2; b = -16; c = +5;
Δ = b2-4ac
Δ = -162-4·2·5
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-6\sqrt{6}}{2*2}=\frac{16-6\sqrt{6}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6\sqrt{6}}{2*2}=\frac{16+6\sqrt{6}}{4}
$