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3x^2-24x=-21
We move all terms to the left:
3x^2-24x-(-21)=0
We add all the numbers together, and all the variables
3x^2-24x+21=0
a = 3; b = -24; c = +21;
Δ = b2-4ac
Δ = -242-4·3·21
Δ = 324
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{324}=18$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-18}{2*3}=\frac{6}{6} =1 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+18}{2*3}=\frac{42}{6} =7 $
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