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(x+2)(x-7)=-3(x+4)
We move all terms to the left:
(x+2)(x-7)-(-3(x+4))=0
We multiply parentheses ..
(+x^2-7x+2x-14)-(-3(x+4))=0
We calculate terms in parentheses: -(-3(x+4)), so:We get rid of parentheses
-3(x+4)
We multiply parentheses
-3x-12
Back to the equation:
-(-3x-12)
x^2-7x+2x+3x-14+12=0
We add all the numbers together, and all the variables
x^2-2x-2=0
a = 1; b = -2; c = -2;
Δ = b2-4ac
Δ = -22-4·1·(-2)
Δ = 12
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{12}=\sqrt{4*3}=\sqrt{4}*\sqrt{3}=2\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{3}}{2*1}=\frac{2-2\sqrt{3}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{3}}{2*1}=\frac{2+2\sqrt{3}}{2} $
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