12.3(6x+10)=7(3/7x-2)

Solution for 12.3(6x+10)=7(3/7x-2) equation:

12.3(6x+10)=7(3/7x-2)

We move all terms to the left:

12.3(6x+10)-(7(3/7x-2))=0


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

x∈R


We multiply parentheses

73.8x-(7(3/7x-2))+123=0

We multiply all the terms by the denominator


(73.8x)*7x+123*7x-2))-(7(3-2))=0

We add all the numbers together, and all the variables

(+73.8x)*7x+123*7x-2))-(71)=0

We add all the numbers together, and all the variables

(+73.8x)*7x+123*7x=0

We multiply parentheses

511x^2+123*7x=0

Wy multiply elements

511x^2+861x=0

a = 511; b = 861; c = 0;
Δ = b2-4ac
Δ = 8612-4·511·0
Δ = 741321
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{741321}=861$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(861)-861}{2*511}=\frac{-1722}{1022}
=-1+50/73
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(861)+861}{2*511}=\frac{0}{1022}
=0
$