7x=-14x^2

Solution for 7x=-14x^2 equation:

7x=-14x^2

We move all terms to the left:

7x-(-14x^2)=0

We get rid of parentheses

14x^2+7x=0

a = 14; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·14·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*14}=\frac{-14}{28}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*14}=\frac{0}{28}
=0
$