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4x(x-1)+5=3+2x
We move all terms to the left:
4x(x-1)+5-(3+2x)=0
We add all the numbers together, and all the variables
4x(x-1)-(2x+3)+5=0
We multiply parentheses
4x^2-4x-(2x+3)+5=0
We get rid of parentheses
4x^2-4x-2x-3+5=0
We add all the numbers together, and all the variables
4x^2-6x+2=0
a = 4; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·4·2
Δ = 4
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{4}=2$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2}{2*4}=\frac{4}{8} =1/2 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2}{2*4}=\frac{8}{8} =1 $
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