(42+x)(x)=400

Solution for (42+x)(x)=400 equation:

(42+x)(x)=400

We move all terms to the left:

(42+x)(x)-(400)=0

We add all the numbers together, and all the variables

(x+42)x-400=0

We multiply parentheses

x^2+42x-400=0

a = 1; b = 42; c = -400;
Δ = b2-4ac
Δ = 422-4·1·(-400)
Δ = 3364
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3364}=58$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(42)-58}{2*1}=\frac{-100}{2}
=-50
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(42)+58}{2*1}=\frac{16}{2}
=8
$