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(7x+19)x=23
We move all terms to the left:
(7x+19)x-(23)=0
We multiply parentheses
7x^2+19x-23=0
a = 7; b = 19; c = -23;
Δ = b2-4ac
Δ = 192-4·7·(-23)
Δ = 1005
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{-(19)-\sqrt{1005}}{2*7}=\frac{-19-\sqrt{1005}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(19)+\sqrt{1005}}{2*7}=\frac{-19+\sqrt{1005}}{14} $
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