2x^2+21x+10=165

Solution for 2x^2+21x+10=165 equation:

2x^2+21x+10=165

We move all terms to the left:

2x^2+21x+10-(165)=0

We add all the numbers together, and all the variables

2x^2+21x-155=0

a = 2; b = 21; c = -155;
Δ = b2-4ac
Δ = 212-4·2·(-155)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-41}{2*2}=\frac{-62}{4}
=-15+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+41}{2*2}=\frac{20}{4}
=5
$