2x^2-8x+15=7.5

Solution for 2x^2-8x+15=7.5 equation:

2x^2-8x+15=7.5

We move all terms to the left:

2x^2-8x+15-(7.5)=0

We add all the numbers together, and all the variables

2x^2-8x+7.5=0

a = 2; b = -8; c = +7.5;
Δ = b2-4ac
Δ = -82-4·2·7.5
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2}{2*2}=\frac{6}{4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2}{2*2}=\frac{10}{4}
=2+1/2
$