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5x(x+96)=18
We move all terms to the left:
5x(x+96)-(18)=0
We multiply parentheses
5x^2+480x-18=0
a = 5; b = 480; c = -18;
Δ = b2-4ac
Δ = 4802-4·5·(-18)
Δ = 230760
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{230760}=\sqrt{36*6410}=\sqrt{36}*\sqrt{6410}=6\sqrt{6410}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(480)-6\sqrt{6410}}{2*5}=\frac{-480-6\sqrt{6410}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(480)+6\sqrt{6410}}{2*5}=\frac{-480+6\sqrt{6410}}{10} $
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