10(-3/5x+4)=-21(2/7x-1)

Solution for 10(-3/5x+4)=-21(2/7x-1) equation:

10(-3/5x+4)=-21(2/7x-1)

We move all terms to the left:

10(-3/5x+4)-(-21(2/7x-1))=0


Domain of the equation: 5x+4)!=0

x∈R



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

x∈R


We multiply parentheses

-30x-(-21(2/7x-1))+40=0

We multiply all the terms by the denominator


-30x*7x+40*7x-1))-(-21(2-1))=0

We add all the numbers together, and all the variables

-30x*7x+40*7x-1))-(-211)=0

We add all the numbers together, and all the variables

-30x*7x+40*7x=0

Wy multiply elements

-210x^2+280x=0

a = -210; b = 280; c = 0;
Δ = b2-4ac
Δ = 2802-4·(-210)·0
Δ = 78400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{78400}=280$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(280)-280}{2*-210}=\frac{-560}{-420}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(280)+280}{2*-210}=\frac{0}{-420}
=0
$