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