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x(6x-46)=-7
We move all terms to the left:
x(6x-46)-(-7)=0
We add all the numbers together, and all the variables
x(6x-46)+7=0
We multiply parentheses
6x^2-46x+7=0
a = 6; b = -46; c = +7;
Δ = b2-4ac
Δ = -462-4·6·7
Δ = 1948
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1948}=\sqrt{4*487}=\sqrt{4}*\sqrt{487}=2\sqrt{487}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-46)-2\sqrt{487}}{2*6}=\frac{46-2\sqrt{487}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-46)+2\sqrt{487}}{2*6}=\frac{46+2\sqrt{487}}{12} $
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