5x-7=2/3x+20

Solution for 5x-7=2/3x+20 equation:

5x-7=2/3x+20

We move all terms to the left:

5x-7-(2/3x+20)=0


Domain of the equation: 3x+20)!=0

x∈R


We get rid of parentheses

5x-2/3x-20-7=0

We multiply all the terms by the denominator


5x*3x-20*3x-7*3x-2=0

Wy multiply elements

15x^2-60x-21x-2=0

We add all the numbers together, and all the variables

15x^2-81x-2=0

a = 15; b = -81; c = -2;
Δ = b2-4ac
Δ = -812-4·15·(-2)
Δ = 6681
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{-(-81)-\sqrt{6681}}{2*15}=\frac{81-\sqrt{6681}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-81)+\sqrt{6681}}{2*15}=\frac{81+\sqrt{6681}}{30}
$