4(6x^2-31x+5)=0

Solution for 4(6x^2-31x+5)=0 equation:

4(6x^2-31x+5)=0

We multiply parentheses

24x^2-124x+20=0

a = 24; b = -124; c = +20;
Δ = b2-4ac
Δ = -1242-4·24·20
Δ = 13456
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{13456}=116$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-124)-116}{2*24}=\frac{8}{48}
=1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-124)+116}{2*24}=\frac{240}{48}
=5
$