(5x-1)(5x+2)=14

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Solution for (5x-1)(5x+2)=14 equation:



(5x-1)(5x+2)=14
We move all terms to the left:
(5x-1)(5x+2)-(14)=0
We multiply parentheses ..
(+25x^2+10x-5x-2)-14=0
We get rid of parentheses
25x^2+10x-5x-2-14=0
We add all the numbers together, and all the variables
25x^2+5x-16=0
a = 25; b = 5; c = -16;
Δ = b2-4ac
Δ = 52-4·25·(-16)
Δ = 1625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{1625}=\sqrt{25*65}=\sqrt{25}*\sqrt{65}=5\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5\sqrt{65}}{2*25}=\frac{-5-5\sqrt{65}}{50} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5\sqrt{65}}{2*25}=\frac{-5+5\sqrt{65}}{50} $

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