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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x+1)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


96x^2/200x^2+100x/200x^2+(-150x)/200x^2-1=0

We multiply all the terms by the denominator


96x^2+100x+(-150x)-1*200x^2=0

Wy multiply elements

96x^2-200x^2+100x+(-150x)=0

We get rid of parentheses

96x^2-200x^2+100x-150x=0

We add all the numbers together, and all the variables

-104x^2-50x=0

a = -104; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·(-104)·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*-104}=\frac{0}{-208}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*-104}=\frac{100}{-208}
=-25/52
$