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2x(3x-3)+7(3x-3)=4
We move all terms to the left:
2x(3x-3)+7(3x-3)-(4)=0
We multiply parentheses
6x^2-6x+21x-21-4=0
We add all the numbers together, and all the variables
6x^2+15x-25=0
a = 6; b = 15; c = -25;
Δ = b2-4ac
Δ = 152-4·6·(-25)
Δ = 825
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{825}=\sqrt{25*33}=\sqrt{25}*\sqrt{33}=5\sqrt{33}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{33}}{2*6}=\frac{-15-5\sqrt{33}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{33}}{2*6}=\frac{-15+5\sqrt{33}}{12} $
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