2(3x+7)x=70

Solution for 2(3x+7)x=70 equation:

2(3x+7)x=70

We move all terms to the left:

2(3x+7)x-(70)=0

We multiply parentheses

6x^2+14x-70=0

a = 6; b = 14; c = -70;
Δ = b2-4ac
Δ = 142-4·6·(-70)
Δ = 1876
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:

$\sqrt{\Delta}=\sqrt{1876}=\sqrt{4*469}=\sqrt{4}*\sqrt{469}=2\sqrt{469}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{469}}{2*6}=\frac{-14-2\sqrt{469}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{469}}{2*6}=\frac{-14+2\sqrt{469}}{12}
$