x^2-9x=9/2

Solution for x^2-9x=9/2 equation:

x^2-9x=9/2

We move all terms to the left:

x^2-9x-(9/2)=0

We add all the numbers together, and all the variables

x^2-9x-(+9/2)=0

We get rid of parentheses

x^2-9x-9/2=0

We multiply all the terms by the denominator


x^2*2-9x*2-9=0

Wy multiply elements

2x^2-18x-9=0

a = 2; b = -18; c = -9;
Δ = b2-4ac
Δ = -182-4·2·(-9)
Δ = 396
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:

$\sqrt{\Delta}=\sqrt{396}=\sqrt{36*11}=\sqrt{36}*\sqrt{11}=6\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{11}}{2*2}=\frac{18-6\sqrt{11}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{11}}{2*2}=\frac{18+6\sqrt{11}}{4}
$