5x-5+9/4x-3=10

Solution for 5x-5+9/4x-3=10 equation:

5x-5+9/4x-3=10

We move all terms to the left:

5x-5+9/4x-3-(10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

5x+9/4x-18=0

We multiply all the terms by the denominator


5x*4x-18*4x+9=0

Wy multiply elements

20x^2-72x+9=0

a = 20; b = -72; c = +9;
Δ = b2-4ac
Δ = -722-4·20·9
Δ = 4464
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:

$\sqrt{\Delta}=\sqrt{4464}=\sqrt{144*31}=\sqrt{144}*\sqrt{31}=12\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-72)-12\sqrt{31}}{2*20}=\frac{72-12\sqrt{31}}{40}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-72)+12\sqrt{31}}{2*20}=\frac{72+12\sqrt{31}}{40}
$