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 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 = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{7}}{2*2}=\frac{18-6\sqrt{7}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{7}}{2*2}=\frac{18+6\sqrt{7}}{4}
$