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6x^2-7x+8=7
We move all terms to the left:
6x^2-7x+8-(7)=0
We add all the numbers together, and all the variables
6x^2-7x+1=0
a = 6; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·6·1
Δ = 25
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{25}=5$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-5}{2*6}=\frac{2}{12} =1/6 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+5}{2*6}=\frac{12}{12} =1 $
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