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

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



0=(4x-1)(x+6)
We move all terms to the left:
0-((4x-1)(x+6))=0
We add all the numbers together, and all the variables
-((4x-1)(x+6))=0
We multiply parentheses ..
-((+4x^2+24x-1x-6))=0
We calculate terms in parentheses: -((+4x^2+24x-1x-6)), so:
(+4x^2+24x-1x-6)
We get rid of parentheses
4x^2+24x-1x-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{-2}{-8} =1/4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+25}{2*-4}=\frac{48}{-8} =-6 $

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