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5x(x+2)=3x+4
We move all terms to the left:
5x(x+2)-(3x+4)=0
We multiply parentheses
5x^2+10x-(3x+4)=0
We get rid of parentheses
5x^2+10x-3x-4=0
We add all the numbers together, and all the variables
5x^2+7x-4=0
a = 5; b = 7; c = -4;
Δ = b2-4ac
Δ = 72-4·5·(-4)
Δ = 129
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-\sqrt{129}}{2*5}=\frac{-7-\sqrt{129}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{129}}{2*5}=\frac{-7+\sqrt{129}}{10} $
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