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2x(5x-1)-8x=3x+2
We move all terms to the left:
2x(5x-1)-8x-(3x+2)=0
We add all the numbers together, and all the variables
-8x+2x(5x-1)-(3x+2)=0
We multiply parentheses
10x^2-8x-2x-(3x+2)=0
We get rid of parentheses
10x^2-8x-2x-3x-2=0
We add all the numbers together, and all the variables
10x^2-13x-2=0
a = 10; b = -13; c = -2;
Δ = b2-4ac
Δ = -132-4·10·(-2)
Δ = 249
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-\sqrt{249}}{2*10}=\frac{13-\sqrt{249}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+\sqrt{249}}{2*10}=\frac{13+\sqrt{249}}{20} $
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