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15x(x-2)=34
We move all terms to the left:
15x(x-2)-(34)=0
We multiply parentheses
15x^2-30x-34=0
a = 15; b = -30; c = -34;
Δ = b2-4ac
Δ = -302-4·15·(-34)
Δ = 2940
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2940}=\sqrt{196*15}=\sqrt{196}*\sqrt{15}=14\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-14\sqrt{15}}{2*15}=\frac{30-14\sqrt{15}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+14\sqrt{15}}{2*15}=\frac{30+14\sqrt{15}}{30} $
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