(5x-4)-(-2-5x)x=3

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Solution for (5x-4)-(-2-5x)x=3 equation:



(5x-4)-(-2-5x)x=3
We move all terms to the left:
(5x-4)-(-2-5x)x-(3)=0
We add all the numbers together, and all the variables
(5x-4)-(-5x-2)x-3=0
We multiply parentheses
5x^2+(5x-4)+2x-3=0
We get rid of parentheses
5x^2+5x+2x-4-3=0
We add all the numbers together, and all the variables
5x^2+7x-7=0
a = 5; b = 7; c = -7;
Δ = b2-4ac
Δ = 72-4·5·(-7)
Δ = 189
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:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-3\sqrt{21}}{2*5}=\frac{-7-3\sqrt{21}}{10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+3\sqrt{21}}{2*5}=\frac{-7+3\sqrt{21}}{10} $

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