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(x-30)x=90
We move all terms to the left:
(x-30)x-(90)=0
We multiply parentheses
x^2-30x-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:x_{1}=\frac{-b-\sqrt{\Delta}}{2a}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}
The end solution:
\sqrt{\Delta}=\sqrt{1260}=\sqrt{36*35}=\sqrt{36}*\sqrt{35}=6\sqrt{35}x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-6\sqrt{35}}{2*1}=\frac{30-6\sqrt{35}}{2}x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+6\sqrt{35}}{2*1}=\frac{30+6\sqrt{35}}{2}
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