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7x^2=180-x
We move all terms to the left:
7x^2-(180-x)=0
We add all the numbers together, and all the variables
7x^2-(-1x+180)=0
We get rid of parentheses
7x^2+1x-180=0
We add all the numbers together, and all the variables
7x^2+x-180=0
a = 7; b = 1; c = -180;
Δ = b2-4ac
Δ = 12-4·7·(-180)
Δ = 5041
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{5041}=71$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-71}{2*7}=\frac{-72}{14} =-5+1/7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+71}{2*7}=\frac{70}{14} =5 $
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