2x^2-12x+13=45

Solution for 2x^2-12x+13=45 equation:

2x^2-12x+13=45

We move all terms to the left:

2x^2-12x+13-(45)=0

We add all the numbers together, and all the variables

2x^2-12x-32=0

a = 2; b = -12; c = -32;
Δ = b2-4ac
Δ = -122-4·2·(-32)
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-20}{2*2}=\frac{-8}{4}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+20}{2*2}=\frac{32}{4}
=8
$