40x*10x=42000

Solution for 40x*10x=42000 equation:

40x*10x=42000

We move all terms to the left:

40x*10x-(42000)=0

Wy multiply elements

400x^2-42000=0

a = 400; b = 0; c = -42000;
Δ = b2-4ac
Δ = 02-4·400·(-42000)
Δ = 67200000
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:

$\sqrt{\Delta}=\sqrt{67200000}=\sqrt{640000*105}=\sqrt{640000}*\sqrt{105}=800\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-800\sqrt{105}}{2*400}=\frac{0-800\sqrt{105}}{800}
=-\frac{800\sqrt{105}}{800}
=-\sqrt{105}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+800\sqrt{105}}{2*400}=\frac{0+800\sqrt{105}}{800}
=\frac{800\sqrt{105}}{800}
=\sqrt{105}
$