3/4x+1/5=1/2x-7

Solution for 3/4x+1/5=1/2x-7 equation:

3/4x+1/5=1/2x-7

We move all terms to the left:

3/4x+1/5-(1/2x-7)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x-7)!=0

x∈R


We get rid of parentheses

3/4x-1/2x+7+1/5=0

We calculate fractions


16x^2/200x^2+150x/200x^2+(-100x)/200x^2+7=0

We multiply all the terms by the denominator


16x^2+150x+(-100x)+7*200x^2=0

Wy multiply elements

16x^2+1400x^2+150x+(-100x)=0

We get rid of parentheses

16x^2+1400x^2+150x-100x=0

We add all the numbers together, and all the variables

1416x^2+50x=0

a = 1416; b = 50; c = 0;
Δ = b2-4ac
Δ = 502-4·1416·0
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*1416}=\frac{-100}{2832}
=-25/708
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+50}{2*1416}=\frac{0}{2832}
=0
$