5x+7=2/3x+13

Solution for 5x+7=2/3x+13 equation:

5x+7=2/3x+13

We move all terms to the left:

5x+7-(2/3x+13)=0


Domain of the equation: 3x+13)!=0

x∈R


We get rid of parentheses

5x-2/3x-13+7=0

We multiply all the terms by the denominator


5x*3x-13*3x+7*3x-2=0

Wy multiply elements

15x^2-39x+21x-2=0

We add all the numbers together, and all the variables

15x^2-18x-2=0

a = 15; b = -18; c = -2;
Δ = b2-4ac
Δ = -182-4·15·(-2)
Δ = 444
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:

$\sqrt{\Delta}=\sqrt{444}=\sqrt{4*111}=\sqrt{4}*\sqrt{111}=2\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{111}}{2*15}=\frac{18-2\sqrt{111}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{111}}{2*15}=\frac{18+2\sqrt{111}}{30}
$