5(x-7)=2/3x+15

Solution for 5(x-7)=2/3x+15 equation:

5(x-7)=2/3x+15

We move all terms to the left:

5(x-7)-(2/3x+15)=0


Domain of the equation: 3x+15)!=0

x∈R


We multiply parentheses

5x-(2/3x+15)-35=0

We get rid of parentheses

5x-2/3x-15-35=0

We multiply all the terms by the denominator


5x*3x-15*3x-35*3x-2=0

Wy multiply elements

15x^2-45x-105x-2=0

We add all the numbers together, and all the variables

15x^2-150x-2=0

a = 15; b = -150; c = -2;
Δ = b2-4ac
Δ = -1502-4·15·(-2)
Δ = 22620
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:

$\sqrt{\Delta}=\sqrt{22620}=\sqrt{4*5655}=\sqrt{4}*\sqrt{5655}=2\sqrt{5655}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-2\sqrt{5655}}{2*15}=\frac{150-2\sqrt{5655}}{30}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+2\sqrt{5655}}{2*15}=\frac{150+2\sqrt{5655}}{30}
$