3/4x-2/5=1/2x-13

Solution for 3/4x-2/5=1/2x-13 equation:

3/4x-2/5=1/2x-13

We move all terms to the left:

3/4x-2/5-(1/2x-13)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-13)!=0

x∈R


We get rid of parentheses

3/4x-1/2x+13-2/5=0

We calculate fractions


(-32x^2)/200x^2+150x/200x^2+(-100x)/200x^2+13=0

We multiply all the terms by the denominator


(-32x^2)+150x+(-100x)+13*200x^2=0

Wy multiply elements

(-32x^2)+2600x^2+150x+(-100x)=0

We get rid of parentheses

-32x^2+2600x^2+150x-100x=0

We add all the numbers together, and all the variables

2568x^2+50x=0

a = 2568; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·2568·0
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*2568}=\frac{-100}{5136}
=-25/1284
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*2568}=\frac{0}{5136}
=0
$