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2x+1+5x+-4x^2=23
We move all terms to the left:
2x+1+5x+-4x^2-(23)=0
determiningTheFunctionDomain -4x^2+2x+5x+1-23+=0
We add all the numbers together, and all the variables
-4x^2+7x=0
a = -4; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-4)·0
Δ = 49
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{49}=7$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-4}=\frac{-14}{-8} =1+3/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-4}=\frac{0}{-8} =0 $
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