14x(4x+2)=110

Solution for 14x(4x+2)=110 equation:

14x(4x+2)=110

We move all terms to the left:

14x(4x+2)-(110)=0

We multiply parentheses

56x^2+28x-110=0

a = 56; b = 28; c = -110;
Δ = b2-4ac
Δ = 282-4·56·(-110)
Δ = 25424
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:

$\sqrt{\Delta}=\sqrt{25424}=\sqrt{16*1589}=\sqrt{16}*\sqrt{1589}=4\sqrt{1589}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-4\sqrt{1589}}{2*56}=\frac{-28-4\sqrt{1589}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+4\sqrt{1589}}{2*56}=\frac{-28+4\sqrt{1589}}{112}
$