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12x^2+18x=-5
We move all terms to the left:
12x^2+18x-(-5)=0
We add all the numbers together, and all the variables
12x^2+18x+5=0
a = 12; b = 18; c = +5;
Δ = b2-4ac
Δ = 182-4·12·5
Δ = 84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{84}=\sqrt{4*21}=\sqrt{4}*\sqrt{21}=2\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-2\sqrt{21}}{2*12}=\frac{-18-2\sqrt{21}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+2\sqrt{21}}{2*12}=\frac{-18+2\sqrt{21}}{24} $
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