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36^3-7x=6x^2-18x-15
We move all terms to the left:
36^3-7x-(6x^2-18x-15)=0
We add all the numbers together, and all the variables
-7x-(6x^2-18x-15)+46656=0
We get rid of parentheses
-6x^2-7x+18x+15+46656=0
We add all the numbers together, and all the variables
-6x^2+11x+46671=0
a = -6; b = 11; c = +46671;
Δ = b2-4ac
Δ = 112-4·(-6)·46671
Δ = 1120225
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1120225}=\sqrt{25*44809}=\sqrt{25}*\sqrt{44809}=5\sqrt{44809}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-5\sqrt{44809}}{2*-6}=\frac{-11-5\sqrt{44809}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+5\sqrt{44809}}{2*-6}=\frac{-11+5\sqrt{44809}}{-12} $
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