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x(5x-6)=90
We move all terms to the left:
x(5x-6)-(90)=0
We multiply parentheses
5x^2-6x-90=0
a = 5; b = -6; c = -90;
Δ = b2-4ac
Δ = -62-4·5·(-90)
Δ = 1836
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1836}=\sqrt{36*51}=\sqrt{36}*\sqrt{51}=6\sqrt{51}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{51}}{2*5}=\frac{6-6\sqrt{51}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{51}}{2*5}=\frac{6+6\sqrt{51}}{10} $
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