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5x(x-3)-3x-2=45
We move all terms to the left:
5x(x-3)-3x-2-(45)=0
We add all the numbers together, and all the variables
-3x+5x(x-3)-47=0
We multiply parentheses
5x^2-3x-15x-47=0
We add all the numbers together, and all the variables
5x^2-18x-47=0
a = 5; b = -18; c = -47;
Δ = b2-4ac
Δ = -182-4·5·(-47)
Δ = 1264
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1264}=\sqrt{16*79}=\sqrt{16}*\sqrt{79}=4\sqrt{79}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-4\sqrt{79}}{2*5}=\frac{18-4\sqrt{79}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+4\sqrt{79}}{2*5}=\frac{18+4\sqrt{79}}{10} $
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