7x^2+9x+2=20

Solution for 7x^2+9x+2=20 equation:

7x^2+9x+2=20

We move all terms to the left:

7x^2+9x+2-(20)=0

We add all the numbers together, and all the variables

7x^2+9x-18=0

a = 7; b = 9; c = -18;
Δ = b2-4ac
Δ = 92-4·7·(-18)
Δ = 585
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{585}=\sqrt{9*65}=\sqrt{9}*\sqrt{65}=3\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-3\sqrt{65}}{2*7}=\frac{-9-3\sqrt{65}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+3\sqrt{65}}{2*7}=\frac{-9+3\sqrt{65}}{14}
$