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

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

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

We move all terms to the left:

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


Domain of the equation: 7(x+1)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(20x-40)/(28x+28)+(-21xx/(28x+28)=0


We calculate terms in parentheses: +(-21xx/(28x+28), so:

-21xx/(28x+28

We multiply all the terms by the denominator


-21xx

Back to the equation:

+(-21xx)


We get rid of parentheses

(20x-40)/(28x+28)-21xx=0

We multiply all the terms by the denominator


(20x-40)-21xx*(28x+28)=0

We multiply parentheses

-588x^2+(20x-40)-588x=0

We get rid of parentheses

-588x^2+20x-588x-40=0

We add all the numbers together, and all the variables

-588x^2-568x-40=0

a = -588; b = -568; c = -40;
Δ = b2-4ac
Δ = -5682-4·(-588)·(-40)
Δ = 228544
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{228544}=\sqrt{64*3571}=\sqrt{64}*\sqrt{3571}=8\sqrt{3571}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-568)-8\sqrt{3571}}{2*-588}=\frac{568-8\sqrt{3571}}{-1176}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-568)+8\sqrt{3571}}{2*-588}=\frac{568+8\sqrt{3571}}{-1176}
$