(x+2)(x-3)=175

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Solution for (x+2)(x-3)=175 equation:



(X+2)(X-3)=175
We move all terms to the left:
(X+2)(X-3)-(175)=0
We multiply parentheses ..
(+X^2-3X+2X-6)-175=0
We get rid of parentheses
X^2-3X+2X-6-175=0
We add all the numbers together, and all the variables
X^2-1X-181=0
a = 1; b = -1; c = -181;
Δ = b2-4ac
Δ = -12-4·1·(-181)
Δ = 725
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:
$\sqrt{\Delta}=\sqrt{725}=\sqrt{25*29}=\sqrt{25}*\sqrt{29}=5\sqrt{29}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-5\sqrt{29}}{2*1}=\frac{1-5\sqrt{29}}{2} $
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+5\sqrt{29}}{2*1}=\frac{1+5\sqrt{29}}{2} $

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