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x+5x(x+5)=180
We move all terms to the left:
x+5x(x+5)-(180)=0
We multiply parentheses
5x^2+x+25x-180=0
We add all the numbers together, and all the variables
5x^2+26x-180=0
a = 5; b = 26; c = -180;
Δ = b2-4ac
Δ = 262-4·5·(-180)
Δ = 4276
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4276}=\sqrt{4*1069}=\sqrt{4}*\sqrt{1069}=2\sqrt{1069}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{1069}}{2*5}=\frac{-26-2\sqrt{1069}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{1069}}{2*5}=\frac{-26+2\sqrt{1069}}{10} $
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