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3x(2x-7)=4x+7
We move all terms to the left:
3x(2x-7)-(4x+7)=0
We multiply parentheses
6x^2-21x-(4x+7)=0
We get rid of parentheses
6x^2-21x-4x-7=0
We add all the numbers together, and all the variables
6x^2-25x-7=0
a = 6; b = -25; c = -7;
Δ = b2-4ac
Δ = -252-4·6·(-7)
Δ = 793
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{-(-25)-\sqrt{793}}{2*6}=\frac{25-\sqrt{793}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+\sqrt{793}}{2*6}=\frac{25+\sqrt{793}}{12} $
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