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5x(x+2)+4x=6x+17
We move all terms to the left:
5x(x+2)+4x-(6x+17)=0
We add all the numbers together, and all the variables
4x+5x(x+2)-(6x+17)=0
We multiply parentheses
5x^2+4x+10x-(6x+17)=0
We get rid of parentheses
5x^2+4x+10x-6x-17=0
We add all the numbers together, and all the variables
5x^2+8x-17=0
a = 5; b = 8; c = -17;
Δ = b2-4ac
Δ = 82-4·5·(-17)
Δ = 404
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-2\sqrt{101}}{2*5}=\frac{-8-2\sqrt{101}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+2\sqrt{101}}{2*5}=\frac{-8+2\sqrt{101}}{10} $
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