4/5x+3/4=5/2x-1

Solution for 4/5x+3/4=5/2x-1 equation:

4/5x+3/4=5/2x-1

We move all terms to the left:

4/5x+3/4-(5/2x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x-1)!=0

x∈R


We get rid of parentheses

4/5x-5/2x+1+3/4=0

We calculate fractions


60x^2/160x^2+128x/160x^2+(-400x)/160x^2+1=0

We multiply all the terms by the denominator


60x^2+128x+(-400x)+1*160x^2=0

Wy multiply elements

60x^2+160x^2+128x+(-400x)=0

We get rid of parentheses

60x^2+160x^2+128x-400x=0

We add all the numbers together, and all the variables

220x^2-272x=0

a = 220; b = -272; c = 0;
Δ = b2-4ac
Δ = -2722-4·220·0
Δ = 73984
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{73984}=272$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-272)-272}{2*220}=\frac{0}{440}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-272)+272}{2*220}=\frac{544}{440}
=1+13/55
$