A/7x+5=3x+13

Solution for A/7x+5=3x+13 equation:

/7A+5=3A+13

We move all terms to the left:

/7A+5-(3A+13)=0


Domain of the equation: 7A!=0

A!=0/7

A!=0

A∈R


We get rid of parentheses

/7A-3A-13+5=0

We multiply all the terms by the denominator


-3A*7A-13*7A+5*7A+=0

We add all the numbers together, and all the variables

-3A*7A-13*7A+5*7A=0

Wy multiply elements

-21A^2-91A+35A=0

We add all the numbers together, and all the variables

-21A^2-56A=0

a = -21; b = -56; c = 0;
Δ = b2-4ac
Δ = -562-4·(-21)·0
Δ = 3136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3136}=56$
$A_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-56}{2*-21}=\frac{0}{-42}
=0
$
$A_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+56}{2*-21}=\frac{112}{-42}
=-2+2/3
$