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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 5x-7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-15x)/20x^2+(-8x)/20x^2+7+5=0

We add all the numbers together, and all the variables

(-15x)/20x^2+(-8x)/20x^2+12=0

We multiply all the terms by the denominator


(-15x)+(-8x)+12*20x^2=0

Wy multiply elements

240x^2+(-15x)+(-8x)=0

We get rid of parentheses

240x^2-15x-8x=0

We add all the numbers together, and all the variables

240x^2-23x=0

a = 240; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·240·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*240}=\frac{0}{480}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*240}=\frac{46}{480}
=23/240
$