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4x^2-17x+23=4x+3
We move all terms to the left:
4x^2-17x+23-(4x+3)=0
We get rid of parentheses
4x^2-17x-4x-3+23=0
We add all the numbers together, and all the variables
4x^2-21x+20=0
a = 4; b = -21; c = +20;
Δ = b2-4ac
Δ = -212-4·4·20
Δ = 121
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{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-11}{2*4}=\frac{10}{8} =1+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+11}{2*4}=\frac{32}{8} =4 $
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