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5x(x+1)+3x+2=6x+4
We move all terms to the left:
5x(x+1)+3x+2-(6x+4)=0
We add all the numbers together, and all the variables
3x+5x(x+1)-(6x+4)+2=0
We multiply parentheses
5x^2+3x+5x-(6x+4)+2=0
We get rid of parentheses
5x^2+3x+5x-6x-4+2=0
We add all the numbers together, and all the variables
5x^2+2x-2=0
a = 5; b = 2; c = -2;
Δ = b2-4ac
Δ = 22-4·5·(-2)
Δ = 44
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{11}}{2*5}=\frac{-2-2\sqrt{11}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{11}}{2*5}=\frac{-2+2\sqrt{11}}{10} $
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