7x-5/2x-5=0

Solution for 7x-5/2x-5=0 equation:

7x-5/2x-5=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


7x*2x-5*2x-5=0

Wy multiply elements

14x^2-10x-5=0

a = 14; b = -10; c = -5;
Δ = b2-4ac
Δ = -102-4·14·(-5)
Δ = 380
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:

$\sqrt{\Delta}=\sqrt{380}=\sqrt{4*95}=\sqrt{4}*\sqrt{95}=2\sqrt{95}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{95}}{2*14}=\frac{10-2\sqrt{95}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{95}}{2*14}=\frac{10+2\sqrt{95}}{28}
$