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7x(x+20)=180
We move all terms to the left:
7x(x+20)-(180)=0
We multiply parentheses
7x^2+140x-180=0
a = 7; b = 140; c = -180;
Δ = b2-4ac
Δ = 1402-4·7·(-180)
Δ = 24640
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24640}=\sqrt{64*385}=\sqrt{64}*\sqrt{385}=8\sqrt{385}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(140)-8\sqrt{385}}{2*7}=\frac{-140-8\sqrt{385}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(140)+8\sqrt{385}}{2*7}=\frac{-140+8\sqrt{385}}{14} $
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