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6x^2+6x=25-7x+16
We move all terms to the left:
6x^2+6x-(25-7x+16)=0
We add all the numbers together, and all the variables
6x^2+6x-(-7x+41)=0
We get rid of parentheses
6x^2+6x+7x-41=0
We add all the numbers together, and all the variables
6x^2+13x-41=0
a = 6; b = 13; c = -41;
Δ = b2-4ac
Δ = 132-4·6·(-41)
Δ = 1153
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{-(13)-\sqrt{1153}}{2*6}=\frac{-13-\sqrt{1153}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+\sqrt{1153}}{2*6}=\frac{-13+\sqrt{1153}}{12} $
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