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-5x(1-3x)+2x=6
We move all terms to the left:
-5x(1-3x)+2x-(6)=0
We add all the numbers together, and all the variables
-5x(-3x+1)+2x-6=0
We add all the numbers together, and all the variables
2x-5x(-3x+1)-6=0
We multiply parentheses
15x^2+2x-5x-6=0
We add all the numbers together, and all the variables
15x^2-3x-6=0
a = 15; b = -3; c = -6;
Δ = b2-4ac
Δ = -32-4·15·(-6)
Δ = 369
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{41}}{2*15}=\frac{3-3\sqrt{41}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{41}}{2*15}=\frac{3+3\sqrt{41}}{30} $
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