X+9/2x-3=4

Solution for X+9/2x-3=4 equation:

X+9/2X-3=4

We move all terms to the left:

X+9/2X-3-(4)=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+9/2X-7=0

We multiply all the terms by the denominator


X*2X-7*2X+9=0

Wy multiply elements

2X^2-14X+9=0

a = 2; b = -14; c = +9;
Δ = b2-4ac
Δ = -142-4·2·9
Δ = 124
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:

$\sqrt{\Delta}=\sqrt{124}=\sqrt{4*31}=\sqrt{4}*\sqrt{31}=2\sqrt{31}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{31}}{2*2}=\frac{14-2\sqrt{31}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{31}}{2*2}=\frac{14+2\sqrt{31}}{4}
$