(X+5)(x-8)=-30

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Solution for (X+5)(x-8)=-30 equation:



(X+5)(X-8)=-30
We move all terms to the left:
(X+5)(X-8)-(-30)=0
We add all the numbers together, and all the variables
(X+5)(X-8)+30=0
We multiply parentheses ..
(+X^2-8X+5X-40)+30=0
We get rid of parentheses
X^2-8X+5X-40+30=0
We add all the numbers together, and all the variables
X^2-3X-10=0
a = 1; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·1·(-10)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-7}{2*1}=\frac{-4}{2} =-2 $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+7}{2*1}=\frac{10}{2} =5 $

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