42=(x+4)(2x)

Solution for 42=(x+4)(2x) equation:

42=(x+4)(2x)

We move all terms to the left:

42-((x+4)(2x))=0


We calculate terms in parentheses: -((x+4)2x), so:

(x+4)2x

We multiply parentheses

2x^2+8x

Back to the equation:

-(2x^2+8x)


We get rid of parentheses

-2x^2-8x+42=0

a = -2; b = -8; c = +42;
Δ = b2-4ac
Δ = -82-4·(-2)·42
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-20}{2*-2}=\frac{-12}{-4}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+20}{2*-2}=\frac{28}{-4}
=-7
$