4-7/10x=1/5x-11

Solution for 4-7/10x=1/5x-11 equation:

4-7/10x=1/5x-11

We move all terms to the left:

4-7/10x-(1/5x-11)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



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

x∈R


We get rid of parentheses

-7/10x-1/5x+11+4=0

We calculate fractions


(-35x)/50x^2+(-10x)/50x^2+11+4=0

We add all the numbers together, and all the variables

(-35x)/50x^2+(-10x)/50x^2+15=0

We multiply all the terms by the denominator


(-35x)+(-10x)+15*50x^2=0

Wy multiply elements

750x^2+(-35x)+(-10x)=0

We get rid of parentheses

750x^2-35x-10x=0

We add all the numbers together, and all the variables

750x^2-45x=0

a = 750; b = -45; c = 0;
Δ = b2-4ac
Δ = -452-4·750·0
Δ = 2025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2025}=45$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-45}{2*750}=\frac{0}{1500}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+45}{2*750}=\frac{90}{1500}
=3/50
$