4x2-x-3=64

Solution for 4x2-x-3=64 equation:

4x^2-x-3=64

We move all terms to the left:

4x^2-x-3-(64)=0

We add all the numbers together, and all the variables

4x^2-1x-67=0

a = 4; b = -1; c = -67;
Δ = b2-4ac
Δ = -12-4·4·(-67)
Δ = 1073
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{1073}}{2*4}=\frac{1-\sqrt{1073}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{1073}}{2*4}=\frac{1+\sqrt{1073}}{8}
$