(x)(2x+9)=420

Solution for (x)(2x+9)=420 equation:

(x)(2x+9)=420

We move all terms to the left:

(x)(2x+9)-(420)=0

We multiply parentheses

2x^2+9x-420=0

a = 2; b = 9; c = -420;
Δ = b2-4ac
Δ = 92-4·2·(-420)
Δ = 3441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-\sqrt{3441}}{2*2}=\frac{-9-\sqrt{3441}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{3441}}{2*2}=\frac{-9+\sqrt{3441}}{4}
$