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5x(2x-1)=9x+2
We move all terms to the left:
5x(2x-1)-(9x+2)=0
We multiply parentheses
10x^2-5x-(9x+2)=0
We get rid of parentheses
10x^2-5x-9x-2=0
We add all the numbers together, and all the variables
10x^2-14x-2=0
a = 10; b = -14; c = -2;
Δ = b2-4ac
Δ = -142-4·10·(-2)
Δ = 276
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{69}}{2*10}=\frac{14-2\sqrt{69}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{69}}{2*10}=\frac{14+2\sqrt{69}}{20} $
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