2x(2x+5)=42

Solution for 2x(2x+5)=42 equation:

2x(2x+5)=42

We move all terms to the left:

2x(2x+5)-(42)=0

We multiply parentheses

4x^2+10x-42=0

a = 4; b = 10; c = -42;
Δ = b2-4ac
Δ = 102-4·4·(-42)
Δ = 772
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:

$\sqrt{\Delta}=\sqrt{772}=\sqrt{4*193}=\sqrt{4}*\sqrt{193}=2\sqrt{193}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{193}}{2*4}=\frac{-10-2\sqrt{193}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{193}}{2*4}=\frac{-10+2\sqrt{193}}{8}
$