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(x+1)(x-2)-3(x+5)=3-5x
We move all terms to the left:
(x+1)(x-2)-3(x+5)-(3-5x)=0
We add all the numbers together, and all the variables
(x+1)(x-2)-3(x+5)-(-5x+3)=0
We multiply parentheses
(x+1)(x-2)-3x-(-5x+3)-15=0
We get rid of parentheses
(x+1)(x-2)-3x+5x-3-15=0
We multiply parentheses ..
(+x^2-2x+x-2)-3x+5x-3-15=0
We add all the numbers together, and all the variables
(+x^2-2x+x-2)+2x-18=0
We get rid of parentheses
x^2-2x+x+2x-2-18=0
We add all the numbers together, and all the variables
x^2+x-20=0
a = 1; b = 1; c = -20;
Δ = b2-4ac
Δ = 12-4·1·(-20)
Δ = 81
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{81}=9$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-9}{2*1}=\frac{-10}{2} =-5 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+9}{2*1}=\frac{8}{2} =4 $
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