0=(x-6)(4x+1)

Solution for 0=(x-6)(4x+1) equation:

0=(x-6)(4x+1)

We move all terms to the left:

0-((x-6)(4x+1))=0

We add all the numbers together, and all the variables

-((x-6)(4x+1))=0

We multiply parentheses ..

-((+4x^2+x-24x-6))=0


We calculate terms in parentheses: -((+4x^2+x-24x-6)), so:

(+4x^2+x-24x-6)

We get rid of parentheses

4x^2+x-24x-6

We add all the numbers together, and all the variables

4x^2-23x-6

Back to the equation:

-(4x^2-23x-6)


We get rid of parentheses

-4x^2+23x+6=0

a = -4; b = 23; c = +6;
Δ = b2-4ac
Δ = 232-4·(-4)·6
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-25}{2*-4}=\frac{-48}{-8}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+25}{2*-4}=\frac{2}{-8}
=-1/4
$