(X-9)x+(2x-5)=180

Solution for (X-9)x+(2x-5)=180 equation:

(X-9)X+(2X-5)=180

We move all terms to the left:

(X-9)X+(2X-5)-(180)=0

We multiply parentheses

X^2-9X+(2X-5)-180=0

We get rid of parentheses

X^2-9X+2X-5-180=0

We add all the numbers together, and all the variables

X^2-7X-185=0

a = 1; b = -7; c = -185;
Δ = b2-4ac
Δ = -72-4·1·(-185)
Δ = 789
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{-(-7)-\sqrt{789}}{2*1}=\frac{7-\sqrt{789}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{789}}{2*1}=\frac{7+\sqrt{789}}{2}
$