X-7/2x-5=-4

Solution for X-7/2x-5=-4 equation:

X-7/2X-5=-4

We move all terms to the left:

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

We multiply all the terms by the denominator


X*2X-1*2X-7=0

Wy multiply elements

2X^2-2X-7=0

a = 2; b = -2; c = -7;
Δ = b2-4ac
Δ = -22-4·2·(-7)
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{15}}{2*2}=\frac{2-2\sqrt{15}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{15}}{2*2}=\frac{2+2\sqrt{15}}{4}
$