(2x+5x)x=420

Solution for (2x+5x)x=420 equation:

(2x+5x)x=420

We move all terms to the left:

(2x+5x)x-(420)=0

We add all the numbers together, and all the variables

(+7x)x-420=0

We multiply parentheses

7x^2-420=0

a = 7; b = 0; c = -420;
Δ = b2-4ac
Δ = 02-4·7·(-420)
Δ = 11760
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:

$\sqrt{\Delta}=\sqrt{11760}=\sqrt{784*15}=\sqrt{784}*\sqrt{15}=28\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{15}}{2*7}=\frac{0-28\sqrt{15}}{14}
=-\frac{28\sqrt{15}}{14}
=-2\sqrt{15}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{15}}{2*7}=\frac{0+28\sqrt{15}}{14}
=\frac{28\sqrt{15}}{14}
=2\sqrt{15}
$