0.5x^2=9x-15

Solution for 0.5x^2=9x-15 equation:

0.5x^2=9x-15

We move all terms to the left:

0.5x^2-(9x-15)=0

We get rid of parentheses

0.5x^2-9x+15=0

a = 0.5; b = -9; c = +15;
Δ = b2-4ac
Δ = -92-4·0.5·15
Δ = 51
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{51}}{2*0.5}=\frac{9-\sqrt{51}}{1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{51}}{2*0.5}=\frac{9+\sqrt{51}}{1}
$