4/5x-3=2/11x-7

Solution for 4/5x-3=2/11x-7 equation:

4/5x-3=2/11x-7

We move all terms to the left:

4/5x-3-(2/11x-7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 11x-7)!=0

x∈R


We get rid of parentheses

4/5x-2/11x+7-3=0

We calculate fractions


44x/55x^2+(-10x)/55x^2+7-3=0

We add all the numbers together, and all the variables

44x/55x^2+(-10x)/55x^2+4=0

We multiply all the terms by the denominator


44x+(-10x)+4*55x^2=0

Wy multiply elements

220x^2+44x+(-10x)=0

We get rid of parentheses

220x^2+44x-10x=0

We add all the numbers together, and all the variables

220x^2+34x=0

a = 220; b = 34; c = 0;
Δ = b2-4ac
Δ = 342-4·220·0
Δ = 1156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1156}=34$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-34}{2*220}=\frac{-68}{440}
=-17/110
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+34}{2*220}=\frac{0}{440}
=0
$