2x^2+6=2x+7.5

Solution for 2x^2+6=2x+7.5 equation:

2x^2+6=2x+7.5

We move all terms to the left:

2x^2+6-(2x+7.5)=0

We get rid of parentheses

2x^2-2x-7.5+6=0

We add all the numbers together, and all the variables

2x^2-2x-1.5=0

a = 2; b = -2; c = -1.5;
Δ = b2-4ac
Δ = -22-4·2·(-1.5)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4}{2*2}=\frac{-2}{4}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4}{2*2}=\frac{6}{4}
=1+1/2
$