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x(3x-26)=90
We move all terms to the left:
x(3x-26)-(90)=0
We multiply parentheses
3x^2-26x-90=0
a = 3; b = -26; c = -90;
Δ = b2-4ac
Δ = -262-4·3·(-90)
Δ = 1756
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1756}=\sqrt{4*439}=\sqrt{4}*\sqrt{439}=2\sqrt{439}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-2\sqrt{439}}{2*3}=\frac{26-2\sqrt{439}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+2\sqrt{439}}{2*3}=\frac{26+2\sqrt{439}}{6} $
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