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(2x+9)(5x)=120
We move all terms to the left:
(2x+9)(5x)-(120)=0
We multiply parentheses
10x^2+45x-120=0
a = 10; b = 45; c = -120;
Δ = b2-4ac
Δ = 452-4·10·(-120)
Δ = 6825
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6825}=\sqrt{25*273}=\sqrt{25}*\sqrt{273}=5\sqrt{273}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(45)-5\sqrt{273}}{2*10}=\frac{-45-5\sqrt{273}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(45)+5\sqrt{273}}{2*10}=\frac{-45+5\sqrt{273}}{20} $
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