-3x2+7x+74x=-3

Solution for -3x2+7x+74x=-3 equation:

-3x^2+7x+74x=-3

We move all terms to the left:

-3x^2+7x+74x-(-3)=0

We add all the numbers together, and all the variables

-3x^2+81x+3=0

a = -3; b = 81; c = +3;
Δ = b2-4ac
Δ = 812-4·(-3)·3
Δ = 6597
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:

$\sqrt{\Delta}=\sqrt{6597}=\sqrt{9*733}=\sqrt{9}*\sqrt{733}=3\sqrt{733}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(81)-3\sqrt{733}}{2*-3}=\frac{-81-3\sqrt{733}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(81)+3\sqrt{733}}{2*-3}=\frac{-81+3\sqrt{733}}{-6}
$