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(23x+1)(27x=19)
We move all terms to the left:
(23x+1)(27x-(19))=0
We multiply parentheses ..
(+621x^2-437x+27x-19)=0
We get rid of parentheses
621x^2-437x+27x-19=0
We add all the numbers together, and all the variables
621x^2-410x-19=0
a = 621; b = -410; c = -19;
Δ = b2-4ac
Δ = -4102-4·621·(-19)
Δ = 215296
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{215296}=464$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-410)-464}{2*621}=\frac{-54}{1242} =-1/23 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-410)+464}{2*621}=\frac{874}{1242} =19/27 $
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