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180=(y-30)y+90
We move all terms to the left:
180-((y-30)y+90)=0
We calculate terms in parentheses: -((y-30)y+90), so:We get rid of parentheses
(y-30)y+90
We multiply parentheses
y^2-30y+90
Back to the equation:
-(y^2-30y+90)
-y^2+30y-90+180=0
We add all the numbers together, and all the variables
-1y^2+30y+90=0
a = -1; b = 30; c = +90;
Δ = b2-4ac
Δ = 302-4·(-1)·90
Δ = 1260
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}$$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{35}}{2*-1}=\frac{-30-6\sqrt{35}}{-2} $$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{35}}{2*-1}=\frac{-30+6\sqrt{35}}{-2} $
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