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x(7x-3)=19
We move all terms to the left:
x(7x-3)-(19)=0
We multiply parentheses
7x^2-3x-19=0
a = 7; b = -3; c = -19;
Δ = b2-4ac
Δ = -32-4·7·(-19)
Δ = 541
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{-(-3)-\sqrt{541}}{2*7}=\frac{3-\sqrt{541}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{541}}{2*7}=\frac{3+\sqrt{541}}{14} $
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