(1/2)9x+18+(8x+9)=180

Solution for (1/2)9x+18+(8x+9)=180 equation:

(1/2)9x+18+(8x+9)=180

We move all terms to the left:

(1/2)9x+18+(8x+9)-(180)=0


Domain of the equation: 2)9x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)9x+(8x+9)+18-180=0

We add all the numbers together, and all the variables

(+1/2)9x+(8x+9)-162=0

We multiply parentheses

9x^2+(8x+9)-162=0

We get rid of parentheses

9x^2+8x+9-162=0

We add all the numbers together, and all the variables

9x^2+8x-153=0

a = 9; b = 8; c = -153;
Δ = b2-4ac
Δ = 82-4·9·(-153)
Δ = 5572
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:

$\sqrt{\Delta}=\sqrt{5572}=\sqrt{4*1393}=\sqrt{4}*\sqrt{1393}=2\sqrt{1393}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{1393}}{2*9}=\frac{-8-2\sqrt{1393}}{18}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{1393}}{2*9}=\frac{-8+2\sqrt{1393}}{18}
$