2x^2-21x+52=-2

Solution for 2x^2-21x+52=-2 equation:

2x^2-21x+52=-2

We move all terms to the left:

2x^2-21x+52-(-2)=0

We add all the numbers together, and all the variables

2x^2-21x+54=0

a = 2; b = -21; c = +54;
Δ = b2-4ac
Δ = -212-4·2·54
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3}{2*2}=\frac{18}{4}
=4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3}{2*2}=\frac{24}{4}
=6
$