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6x^2-16x=13-7x
We move all terms to the left:
6x^2-16x-(13-7x)=0
We add all the numbers together, and all the variables
6x^2-16x-(-7x+13)=0
We get rid of parentheses
6x^2-16x+7x-13=0
We add all the numbers together, and all the variables
6x^2-9x-13=0
a = 6; b = -9; c = -13;
Δ = b2-4ac
Δ = -92-4·6·(-13)
Δ = 393
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{-(-9)-\sqrt{393}}{2*6}=\frac{9-\sqrt{393}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{393}}{2*6}=\frac{9+\sqrt{393}}{12} $
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