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5x(x+4)=3x-5
We move all terms to the left:
5x(x+4)-(3x-5)=0
We multiply parentheses
5x^2+20x-(3x-5)=0
We get rid of parentheses
5x^2+20x-3x+5=0
We add all the numbers together, and all the variables
5x^2+17x+5=0
a = 5; b = 17; c = +5;
Δ = b2-4ac
Δ = 172-4·5·5
Δ = 189
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{189}=\sqrt{9*21}=\sqrt{9}*\sqrt{21}=3\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(17)-3\sqrt{21}}{2*5}=\frac{-17-3\sqrt{21}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(17)+3\sqrt{21}}{2*5}=\frac{-17+3\sqrt{21}}{10} $
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