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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

3x^2-4x-7=0

a = 3; b = -4; c = -7;
Δ = b2-4ac
Δ = -42-4·3·(-7)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-10}{2*3}=\frac{-6}{6}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+10}{2*3}=\frac{14}{6}
=2+1/3
$