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-2x(3x+6)+5x=-12
We move all terms to the left:
-2x(3x+6)+5x-(-12)=0
We add all the numbers together, and all the variables
5x-2x(3x+6)+12=0
We multiply parentheses
-6x^2+5x-12x+12=0
We add all the numbers together, and all the variables
-6x^2-7x+12=0
a = -6; b = -7; c = +12;
Δ = b2-4ac
Δ = -72-4·(-6)·12
Δ = 337
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{337}}{2*-6}=\frac{7-\sqrt{337}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{337}}{2*-6}=\frac{7+\sqrt{337}}{-12} $
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