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26=6x^2-6x-72
We move all terms to the left:
26-(6x^2-6x-72)=0
We get rid of parentheses
-6x^2+6x+72+26=0
We add all the numbers together, and all the variables
-6x^2+6x+98=0
a = -6; b = 6; c = +98;
Δ = b2-4ac
Δ = 62-4·(-6)·98
Δ = 2388
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2388}=\sqrt{4*597}=\sqrt{4}*\sqrt{597}=2\sqrt{597}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{597}}{2*-6}=\frac{-6-2\sqrt{597}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{597}}{2*-6}=\frac{-6+2\sqrt{597}}{-12} $
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