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5x(7x-9)=30
We move all terms to the left:
5x(7x-9)-(30)=0
We multiply parentheses
35x^2-45x-30=0
a = 35; b = -45; c = -30;
Δ = b2-4ac
Δ = -452-4·35·(-30)
Δ = 6225
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6225}=\sqrt{25*249}=\sqrt{25}*\sqrt{249}=5\sqrt{249}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-5\sqrt{249}}{2*35}=\frac{45-5\sqrt{249}}{70} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+5\sqrt{249}}{2*35}=\frac{45+5\sqrt{249}}{70} $
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