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(3x-7)(x-7)=3x
We move all terms to the left:
(3x-7)(x-7)-(3x)=0
We add all the numbers together, and all the variables
-3x+(3x-7)(x-7)=0
We multiply parentheses ..
(+3x^2-21x-7x+49)-3x=0
We get rid of parentheses
3x^2-21x-7x-3x+49=0
We add all the numbers together, and all the variables
3x^2-31x+49=0
a = 3; b = -31; c = +49;
Δ = b2-4ac
Δ = -312-4·3·49
Δ = 373
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-\sqrt{373}}{2*3}=\frac{31-\sqrt{373}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{373}}{2*3}=\frac{31+\sqrt{373}}{6} $
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