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x(4x+20)=180
We move all terms to the left:
x(4x+20)-(180)=0
We multiply parentheses
4x^2+20x-180=0
a = 4; b = 20; c = -180;
Δ = b2-4ac
Δ = 202-4·4·(-180)
Δ = 3280
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{3280}=\sqrt{16*205}=\sqrt{16}*\sqrt{205}=4\sqrt{205}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{205}}{2*4}=\frac{-20-4\sqrt{205}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{205}}{2*4}=\frac{-20+4\sqrt{205}}{8} $
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