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x^2-4x+6=7x
We move all terms to the left:
x^2-4x+6-(7x)=0
We add all the numbers together, and all the variables
x^2-11x+6=0
a = 1; b = -11; c = +6;
Δ = b2-4ac
Δ = -112-4·1·6
Δ = 97
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{-(-11)-\sqrt{97}}{2*1}=\frac{11-\sqrt{97}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{97}}{2*1}=\frac{11+\sqrt{97}}{2} $
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