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(2x-3)(6x+9)=-3
We move all terms to the left:
(2x-3)(6x+9)-(-3)=0
We add all the numbers together, and all the variables
(2x-3)(6x+9)+3=0
We multiply parentheses ..
(+12x^2+18x-18x-27)+3=0
We get rid of parentheses
12x^2+18x-18x-27+3=0
We add all the numbers together, and all the variables
12x^2-24=0
a = 12; b = 0; c = -24;
Δ = b2-4ac
Δ = 02-4·12·(-24)
Δ = 1152
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1152}=\sqrt{576*2}=\sqrt{576}*\sqrt{2}=24\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{2}}{2*12}=\frac{0-24\sqrt{2}}{24} =-\frac{24\sqrt{2}}{24} =-\sqrt{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{2}}{2*12}=\frac{0+24\sqrt{2}}{24} =\frac{24\sqrt{2}}{24} =\sqrt{2} $
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