2x^2/9+x-20=0

Solution for 2x^2/9+x-20=0 equation:

2x^2/9+x-20=0

We multiply all the terms by the denominator


2x^2+x*9-20*9=0

We add all the numbers together, and all the variables

2x^2+x*9-180=0

Wy multiply elements

2x^2+9x-180=0

a = 2; b = 9; c = -180;
Δ = b2-4ac
Δ = 92-4·2·(-180)
Δ = 1521
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1521}=39$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-39}{2*2}=\frac{-48}{4}
=-12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+39}{2*2}=\frac{30}{4}
=7+1/2
$