7x=3x^2+4

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

7x=3x^2+4

We move all terms to the left:

7x-(3x^2+4)=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 = 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{-(7)-1}{2*-3}=\frac{-8}{-6}
=1+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+1}{2*-3}=\frac{-6}{-6}
=1
$