3=4x^2-7x+3

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

3=4x^2-7x+3

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-4x^2+7x=0

a = -4; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-4)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-4}=\frac{-14}{-8}
=1+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-4}=\frac{0}{-8}
=0
$