2x(x+7)=-4x+14

Solution for 2x(x+7)=-4x+14 equation:

2x(x+7)=-4x+14

We move all terms to the left:

2x(x+7)-(-4x+14)=0

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+18x-14=0

a = 2; b = 18; c = -14;
Δ = b2-4ac
Δ = 182-4·2·(-14)
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{109}}{2*2}=\frac{-18-2\sqrt{109}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{109}}{2*2}=\frac{-18+2\sqrt{109}}{4}
$