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-5x(x+1)+3x-3=-14
We move all terms to the left:
-5x(x+1)+3x-3-(-14)=0
We add all the numbers together, and all the variables
3x-5x(x+1)+11=0
We multiply parentheses
-5x^2+3x-5x+11=0
We add all the numbers together, and all the variables
-5x^2-2x+11=0
a = -5; b = -2; c = +11;
Δ = b2-4ac
Δ = -22-4·(-5)·11
Δ = 224
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{14}}{2*-5}=\frac{2-4\sqrt{14}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{14}}{2*-5}=\frac{2+4\sqrt{14}}{-10} $
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