-4*x+7*x^2+3*x=0

Solution for -4*x+7*x^2+3*x=0 equation:

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

We add all the numbers together, and all the variables

7x^2-1x=0

a = 7; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·7·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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