2x(42+2x)=70

Solution for 2x(42+2x)=70 equation:

2x(42+2x)=70

We move all terms to the left:

2x(42+2x)-(70)=0

We add all the numbers together, and all the variables

2x(2x+42)-70=0

We multiply parentheses

4x^2+84x-70=0

a = 4; b = 84; c = -70;
Δ = b2-4ac
Δ = 842-4·4·(-70)
Δ = 8176
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:

$\sqrt{\Delta}=\sqrt{8176}=\sqrt{16*511}=\sqrt{16}*\sqrt{511}=4\sqrt{511}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{511}}{2*4}=\frac{-84-4\sqrt{511}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{511}}{2*4}=\frac{-84+4\sqrt{511}}{8}
$