2x+5=7/5x+11

Solution for 2x+5=7/5x+11 equation:

2x+5=7/5x+11

We move all terms to the left:

2x+5-(7/5x+11)=0


Domain of the equation: 5x+11)!=0

x∈R


We get rid of parentheses

2x-7/5x-11+5=0

We multiply all the terms by the denominator


2x*5x-11*5x+5*5x-7=0

Wy multiply elements

10x^2-55x+25x-7=0

We add all the numbers together, and all the variables

10x^2-30x-7=0

a = 10; b = -30; c = -7;
Δ = b2-4ac
Δ = -302-4·10·(-7)
Δ = 1180
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:

$\sqrt{\Delta}=\sqrt{1180}=\sqrt{4*295}=\sqrt{4}*\sqrt{295}=2\sqrt{295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-2\sqrt{295}}{2*10}=\frac{30-2\sqrt{295}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+2\sqrt{295}}{2*10}=\frac{30+2\sqrt{295}}{20}
$