x=5x2+-6x+-5

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Solution for x=5x2+-6x+-5 equation:



x=5x^2+-6x+-5
We move all terms to the left:
x-(5x^2+-6x+-5)=0
We use the square of the difference formula
x-(5x^2-6x-5)=0
We get rid of parentheses
-5x^2+x+6x+5=0
We add all the numbers together, and all the variables
-5x^2+7x+5=0
a = -5; b = 7; c = +5;
Δ = b2-4ac
Δ = 72-4·(-5)·5
Δ = 149
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{149}}{2*-5}=\frac{-7-\sqrt{149}}{-10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{149}}{2*-5}=\frac{-7+\sqrt{149}}{-10} $

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