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x^2-7x+12=7
We move all terms to the left:
x^2-7x+12-(7)=0
We add all the numbers together, and all the variables
x^2-7x+5=0
a = 1; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·1·5
Δ = 29
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{-(-7)-\sqrt{29}}{2*1}=\frac{7-\sqrt{29}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{29}}{2*1}=\frac{7+\sqrt{29}}{2} $
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