(2x+1)(x)=42

Solution for (2x+1)(x)=42 equation:

(2x+1)(x)=42

We move all terms to the left:

(2x+1)(x)-(42)=0

We multiply parentheses

2x^2+x-42=0

a = 2; b = 1; c = -42;
Δ = b2-4ac
Δ = 12-4·2·(-42)
Δ = 337
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{-(1)-\sqrt{337}}{2*2}=\frac{-1-\sqrt{337}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{337}}{2*2}=\frac{-1+\sqrt{337}}{4}
$