.5x+1=-2/3x+15

Solution for .5x+1=-2/3x+15 equation:

.5x+1=-2/3x+15

We move all terms to the left:

.5x+1-(-2/3x+15)=0


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

x∈R


We get rid of parentheses

.5x+2/3x-15+1=0

We multiply all the terms by the denominator


(.5x)*3x-15*3x+1*3x+2=0

We add all the numbers together, and all the variables

(+.5x)*3x-15*3x+1*3x+2=0

We multiply parentheses

3x^2-15*3x+1*3x+2=0

Wy multiply elements

3x^2-45x+3x+2=0

We add all the numbers together, and all the variables

3x^2-42x+2=0

a = 3; b = -42; c = +2;
Δ = b2-4ac
Δ = -422-4·3·2
Δ = 1740
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:

$\sqrt{\Delta}=\sqrt{1740}=\sqrt{4*435}=\sqrt{4}*\sqrt{435}=2\sqrt{435}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{435}}{2*3}=\frac{42-2\sqrt{435}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{435}}{2*3}=\frac{42+2\sqrt{435}}{6}
$