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0=-7x^2+14x-3
We move all terms to the left:
0-(-7x^2+14x-3)=0
We add all the numbers together, and all the variables
-(-7x^2+14x-3)=0
We get rid of parentheses
7x^2-14x+3=0
a = 7; b = -14; c = +3;
Δ = b2-4ac
Δ = -142-4·7·3
Δ = 112
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{7}}{2*7}=\frac{14-4\sqrt{7}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{7}}{2*7}=\frac{14+4\sqrt{7}}{14} $
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