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5x(3x-7)=10
We move all terms to the left:
5x(3x-7)-(10)=0
We multiply parentheses
15x^2-35x-10=0
a = 15; b = -35; c = -10;
Δ = b2-4ac
Δ = -352-4·15·(-10)
Δ = 1825
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1825}=\sqrt{25*73}=\sqrt{25}*\sqrt{73}=5\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-5\sqrt{73}}{2*15}=\frac{35-5\sqrt{73}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+5\sqrt{73}}{2*15}=\frac{35+5\sqrt{73}}{30} $
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