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5x(5x-30)=180
We move all terms to the left:
5x(5x-30)-(180)=0
We multiply parentheses
25x^2-150x-180=0
a = 25; b = -150; c = -180;
Δ = b2-4ac
Δ = -1502-4·25·(-180)
Δ = 40500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{40500}=\sqrt{8100*5}=\sqrt{8100}*\sqrt{5}=90\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-150)-90\sqrt{5}}{2*25}=\frac{150-90\sqrt{5}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-150)+90\sqrt{5}}{2*25}=\frac{150+90\sqrt{5}}{50} $
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