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6x(5x-3)=15
We move all terms to the left:
6x(5x-3)-(15)=0
We multiply parentheses
30x^2-18x-15=0
a = 30; b = -18; c = -15;
Δ = b2-4ac
Δ = -182-4·30·(-15)
Δ = 2124
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2124}=\sqrt{36*59}=\sqrt{36}*\sqrt{59}=6\sqrt{59}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-6\sqrt{59}}{2*30}=\frac{18-6\sqrt{59}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+6\sqrt{59}}{2*30}=\frac{18+6\sqrt{59}}{60} $
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