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21x^2-69x=-18
We move all terms to the left:
21x^2-69x-(-18)=0
We add all the numbers together, and all the variables
21x^2-69x+18=0
a = 21; b = -69; c = +18;
Δ = b2-4ac
Δ = -692-4·21·18
Δ = 3249
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{3249}=57$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-69)-57}{2*21}=\frac{12}{42} =2/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-69)+57}{2*21}=\frac{126}{42} =3 $
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