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10x(3x+11)=180
We move all terms to the left:
10x(3x+11)-(180)=0
We multiply parentheses
30x^2+110x-180=0
a = 30; b = 110; c = -180;
Δ = b2-4ac
Δ = 1102-4·30·(-180)
Δ = 33700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{33700}=\sqrt{100*337}=\sqrt{100}*\sqrt{337}=10\sqrt{337}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(110)-10\sqrt{337}}{2*30}=\frac{-110-10\sqrt{337}}{60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(110)+10\sqrt{337}}{2*30}=\frac{-110+10\sqrt{337}}{60} $
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