5.6x-7.7=62/3x+12

Solution for 5.6x-7.7=62/3x+12 equation:

5.6x-7.7=62/3x+12

We move all terms to the left:

5.6x-7.7-(62/3x+12)=0


Domain of the equation: 3x+12)!=0

x∈R


We get rid of parentheses

5.6x-62/3x-12-7.7=0

We multiply all the terms by the denominator


(5.6x)*3x-12*3x-(7.7)*3x-62=0

We add all the numbers together, and all the variables

(+5.6x)*3x-12*3x-(7.7)*3x-62=0

We multiply parentheses

15x^2-12*3x-23.1x-62=0

Wy multiply elements

15x^2-36x-23.1x-62=0

We add all the numbers together, and all the variables

15x^2-59.1x-62=0

a = 15; b = -59.1; c = -62;
Δ = b2-4ac
Δ = -59.12-4·15·(-62)
Δ = 7212.81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-59.1)-\sqrt{7212.81}}{2*15}=\frac{59.1-\sqrt{7212.81}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-59.1)+\sqrt{7212.81}}{2*15}=\frac{59.1+\sqrt{7212.81}}{30}
$