(-3)=x2+5x-11

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Solution for (-3)=x2+5x-11 equation:



(-3)=x2+5x-11
We move all terms to the left:
(-3)-(x2+5x-11)=0
We add all the numbers together, and all the variables
-(+x^2+5x-11)+(-3)=0
We add all the numbers together, and all the variables
-(+x^2+5x-11)-3=0
We get rid of parentheses
-x^2-5x+11-3=0
We add all the numbers together, and all the variables
-1x^2-5x+8=0
a = -1; b = -5; c = +8;
Δ = b2-4ac
Δ = -52-4·(-1)·8
Δ = 57
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{-(-5)-\sqrt{57}}{2*-1}=\frac{5-\sqrt{57}}{-2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{57}}{2*-1}=\frac{5+\sqrt{57}}{-2} $

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