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10x(x-3)=90
We move all terms to the left:
10x(x-3)-(90)=0
We multiply parentheses
10x^2-30x-90=0
a = 10; b = -30; c = -90;
Δ = b2-4ac
Δ = -302-4·10·(-90)
Δ = 4500
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4500}=\sqrt{900*5}=\sqrt{900}*\sqrt{5}=30\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30\sqrt{5}}{2*10}=\frac{30-30\sqrt{5}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30\sqrt{5}}{2*10}=\frac{30+30\sqrt{5}}{20} $
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