(6/5)x+13=23-9x

Solution for (6/5)x+13=23-9x equation:

(6/5)x+13=23-9x

We move all terms to the left:

(6/5)x+13-(23-9x)=0


Domain of the equation: 5)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+6/5)x-(-9x+23)+13=0

We multiply parentheses

6x^2-(-9x+23)+13=0

We get rid of parentheses

6x^2+9x-23+13=0

We add all the numbers together, and all the variables

6x^2+9x-10=0

a = 6; b = 9; c = -10;
Δ = b2-4ac
Δ = 92-4·6·(-10)
Δ = 321
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{-(9)-\sqrt{321}}{2*6}=\frac{-9-\sqrt{321}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{321}}{2*6}=\frac{-9+\sqrt{321}}{12}
$