2x-10/5x+11=1

Solution for 2x-10/5x+11=1 equation:

2x-10/5x+11=1

We move all terms to the left:

2x-10/5x+11-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R


We add all the numbers together, and all the variables

2x-10/5x+10=0

We multiply all the terms by the denominator


2x*5x+10*5x-10=0

Wy multiply elements

10x^2+50x-10=0

a = 10; b = 50; c = -10;
Δ = b2-4ac
Δ = 502-4·10·(-10)
Δ = 2900
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:

$\sqrt{\Delta}=\sqrt{2900}=\sqrt{100*29}=\sqrt{100}*\sqrt{29}=10\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-10\sqrt{29}}{2*10}=\frac{-50-10\sqrt{29}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+10\sqrt{29}}{2*10}=\frac{-50+10\sqrt{29}}{20}
$