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(3x-2)x=90
We move all terms to the left:
(3x-2)x-(90)=0
We multiply parentheses
3x^2-2x-90=0
a = 3; b = -2; c = -90;
Δ = b2-4ac
Δ = -22-4·3·(-90)
Δ = 1084
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1084}=\sqrt{4*271}=\sqrt{4}*\sqrt{271}=2\sqrt{271}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{271}}{2*3}=\frac{2-2\sqrt{271}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{271}}{2*3}=\frac{2+2\sqrt{271}}{6} $
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