12=5x^2-3x+4

Solution for 12=5x^2-3x+4 equation:

12=5x^2-3x+4

We move all terms to the left:

12-(5x^2-3x+4)=0

We get rid of parentheses

-5x^2+3x-4+12=0

We add all the numbers together, and all the variables

-5x^2+3x+8=0

a = -5; b = 3; c = +8;
Δ = b2-4ac
Δ = 32-4·(-5)·8
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-13}{2*-5}=\frac{-16}{-10}
=1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+13}{2*-5}=\frac{10}{-10}
=-1
$