X-7/2x-4=1

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

X-7/2X-4=1

We move all terms to the left:

X-7/2X-4-(1)=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-7/2X-5=0

We multiply all the terms by the denominator


X*2X-5*2X-7=0

Wy multiply elements

2X^2-10X-7=0

a = 2; b = -10; c = -7;
Δ = b2-4ac
Δ = -102-4·2·(-7)
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{-(-10)-2\sqrt{39}}{2*2}=\frac{10-2\sqrt{39}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{39}}{2*2}=\frac{10+2\sqrt{39}}{4}
$