4=3x2+7x

Solution for 4=3x2+7x equation:

4=3x^2+7x

We move all terms to the left:

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

We get rid of parentheses

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

a = -3; b = -7; c = +4;
Δ = b2-4ac
Δ = -72-4·(-3)·4
Δ = 97
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{97}}{2*-3}=\frac{7-\sqrt{97}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{97}}{2*-3}=\frac{7+\sqrt{97}}{-6}
$