X/2-3=4x2+x-4

Solution for X/2-3=4x2+x-4 equation:

X/2-3=4X^2+X-4

We move all terms to the left:

X/2-3-(4X^2+X-4)=0

We get rid of parentheses

-4X^2+X/2-X+4-3=0

We multiply all the terms by the denominator


-4X^2*2+X-X*2+4*2-3*2=0

We add all the numbers together, and all the variables

-4X^2*2+X-X*2+2=0

Wy multiply elements

-8X^2+X-2X+2=0

We add all the numbers together, and all the variables

-8X^2-1X+2=0

a = -8; b = -1; c = +2;
Δ = b2-4ac
Δ = -12-4·(-8)·2
Δ = 65
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{-(-1)-\sqrt{65}}{2*-8}=\frac{1-\sqrt{65}}{-16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{65}}{2*-8}=\frac{1+\sqrt{65}}{-16}
$