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1000=3x*x-10x+150
We move all terms to the left:
1000-(3x*x-10x+150)=0
We add all the numbers together, and all the variables
-(-10x+3x*x+150)+1000=0
We get rid of parentheses
10x-3x*x-150+1000=0
We add all the numbers together, and all the variables
10x-3x*x+850=0
Wy multiply elements
-3x^2+10x+850=0
a = -3; b = 10; c = +850;
Δ = b2-4ac
Δ = 102-4·(-3)·850
Δ = 10300
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10300}=\sqrt{100*103}=\sqrt{100}*\sqrt{103}=10\sqrt{103}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-10\sqrt{103}}{2*-3}=\frac{-10-10\sqrt{103}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+10\sqrt{103}}{2*-3}=\frac{-10+10\sqrt{103}}{-6} $
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