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(X-2)(4X+1)-(2X+3)=2
We move all terms to the left:
(X-2)(4X+1)-(2X+3)-(2)=0
We get rid of parentheses
(X-2)(4X+1)-2X-3-2=0
We multiply parentheses ..
(+4X^2+X-8X-2)-2X-3-2=0
We add all the numbers together, and all the variables
(+4X^2+X-8X-2)-2X-5=0
We get rid of parentheses
4X^2+X-8X-2X-2-5=0
We add all the numbers together, and all the variables
4X^2-9X-7=0
a = 4; b = -9; c = -7;
Δ = b2-4ac
Δ = -92-4·4·(-7)
Δ = 193
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{-(-9)-\sqrt{193}}{2*4}=\frac{9-\sqrt{193}}{8} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{193}}{2*4}=\frac{9+\sqrt{193}}{8} $
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