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3x(3x-1)-(4x-7)=16
We move all terms to the left:
3x(3x-1)-(4x-7)-(16)=0
We multiply parentheses
9x^2-3x-(4x-7)-16=0
We get rid of parentheses
9x^2-3x-4x+7-16=0
We add all the numbers together, and all the variables
9x^2-7x-9=0
a = 9; b = -7; c = -9;
Δ = b2-4ac
Δ = -72-4·9·(-9)
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{-(-7)-\sqrt{373}}{2*9}=\frac{7-\sqrt{373}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{373}}{2*9}=\frac{7+\sqrt{373}}{18} $
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