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x(7x-3)=234
We move all terms to the left:
x(7x-3)-(234)=0
We multiply parentheses
7x^2-3x-234=0
a = 7; b = -3; c = -234;
Δ = b2-4ac
Δ = -32-4·7·(-234)
Δ = 6561
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{6561}=81$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-81}{2*7}=\frac{-78}{14} =-5+4/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+81}{2*7}=\frac{84}{14} =6 $
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