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5x(x+4)=3
We move all terms to the left:
5x(x+4)-(3)=0
We multiply parentheses
5x^2+20x-3=0
a = 5; b = 20; c = -3;
Δ = b2-4ac
Δ = 202-4·5·(-3)
Δ = 460
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-2\sqrt{115}}{2*5}=\frac{-20-2\sqrt{115}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+2\sqrt{115}}{2*5}=\frac{-20+2\sqrt{115}}{10} $
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