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3x^2-9x(2x+2)+4=7
We move all terms to the left:
3x^2-9x(2x+2)+4-(7)=0
We add all the numbers together, and all the variables
3x^2-9x(2x+2)-3=0
We multiply parentheses
3x^2-18x^2-18x-3=0
We add all the numbers together, and all the variables
-15x^2-18x-3=0
a = -15; b = -18; c = -3;
Δ = b2-4ac
Δ = -182-4·(-15)·(-3)
Δ = 144
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{144}=12$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-12}{2*-15}=\frac{6}{-30} =-1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+12}{2*-15}=\frac{30}{-30} =-1 $
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