2(2x-7)+2(3x2+4x)=0

Solution for 2(2x-7)+2(3x2+4x)=0 equation:

2(2x-7)+2(3x^2+4x)=0

We multiply parentheses

6x^2+4x+8x-14=0

We add all the numbers together, and all the variables

6x^2+12x-14=0

a = 6; b = 12; c = -14;
Δ = b2-4ac
Δ = 122-4·6·(-14)
Δ = 480
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:

$\sqrt{\Delta}=\sqrt{480}=\sqrt{16*30}=\sqrt{16}*\sqrt{30}=4\sqrt{30}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{30}}{2*6}=\frac{-12-4\sqrt{30}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{30}}{2*6}=\frac{-12+4\sqrt{30}}{12}
$