x+x(40/100)=420

Solution for x+x(40/100)=420 equation:

x+x(40/100)=420

We move all terms to the left:

x+x(40/100)-(420)=0

We add all the numbers together, and all the variables

x+x(+40/100)-420=0

We multiply parentheses

40x^2+x-420=0

a = 40; b = 1; c = -420;
Δ = b2-4ac
Δ = 12-4·40·(-420)
Δ = 67201
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{67201}}{2*40}=\frac{-1-\sqrt{67201}}{80}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{67201}}{2*40}=\frac{-1+\sqrt{67201}}{80}
$