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(4x-3)(x+1)=15
We move all terms to the left:
(4x-3)(x+1)-(15)=0
We multiply parentheses ..
(+4x^2+4x-3x-3)-15=0
We get rid of parentheses
4x^2+4x-3x-3-15=0
We add all the numbers together, and all the variables
4x^2+x-18=0
a = 4; b = 1; c = -18;
Δ = b2-4ac
Δ = 12-4·4·(-18)
Δ = 289
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{289}=17$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-17}{2*4}=\frac{-18}{8} =-2+1/4 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+17}{2*4}=\frac{16}{8} =2 $
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