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5x^2-21x+11=7
We move all terms to the left:
5x^2-21x+11-(7)=0
We add all the numbers together, and all the variables
5x^2-21x+4=0
a = 5; b = -21; c = +4;
Δ = b2-4ac
Δ = -212-4·5·4
Δ = 361
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{361}=19$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-19}{2*5}=\frac{2}{10} =1/5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+19}{2*5}=\frac{40}{10} =4 $
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