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7x^2-48x+97=72-81x+1x^2
We move all terms to the left:
7x^2-48x+97-(72-81x+1x^2)=0
We get rid of parentheses
7x^2-1x^2+81x-48x-72+97=0
We add all the numbers together, and all the variables
6x^2+33x+25=0
a = 6; b = 33; c = +25;
Δ = b2-4ac
Δ = 332-4·6·25
Δ = 489
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{-(33)-\sqrt{489}}{2*6}=\frac{-33-\sqrt{489}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+\sqrt{489}}{2*6}=\frac{-33+\sqrt{489}}{12} $
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