2x^2+20x=42

Solution for 2x^2+20x=42 equation:

2x^2+20x=42

We move all terms to the left:

2x^2+20x-(42)=0

a = 2; b = 20; c = -42;
Δ = b2-4ac
Δ = 202-4·2·(-42)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{46}}{2*2}=\frac{-20-4\sqrt{46}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{46}}{2*2}=\frac{-20+4\sqrt{46}}{4}
$