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7x(x-3)=2(x-4)
We move all terms to the left:
7x(x-3)-(2(x-4))=0
We multiply parentheses
7x^2-21x-(2(x-4))=0
We calculate terms in parentheses: -(2(x-4)), so:We get rid of parentheses
2(x-4)
We multiply parentheses
2x-8
Back to the equation:
-(2x-8)
7x^2-21x-2x+8=0
We add all the numbers together, and all the variables
7x^2-23x+8=0
a = 7; b = -23; c = +8;
Δ = b2-4ac
Δ = -232-4·7·8
Δ = 305
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{-(-23)-\sqrt{305}}{2*7}=\frac{23-\sqrt{305}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{305}}{2*7}=\frac{23+\sqrt{305}}{14} $
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