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3x(x-10)+30=90
We move all terms to the left:
3x(x-10)+30-(90)=0
We add all the numbers together, and all the variables
3x(x-10)-60=0
We multiply parentheses
3x^2-30x-60=0
a = 3; b = -30; c = -60;
Δ = b2-4ac
Δ = -302-4·3·(-60)
Δ = 1620
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1620}=\sqrt{324*5}=\sqrt{324}*\sqrt{5}=18\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-18\sqrt{5}}{2*3}=\frac{30-18\sqrt{5}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+18\sqrt{5}}{2*3}=\frac{30+18\sqrt{5}}{6} $
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