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5x^2-2x-27=18
We move all terms to the left:
5x^2-2x-27-(18)=0
We add all the numbers together, and all the variables
5x^2-2x-45=0
a = 5; b = -2; c = -45;
Δ = b2-4ac
Δ = -22-4·5·(-45)
Δ = 904
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{904}=\sqrt{4*226}=\sqrt{4}*\sqrt{226}=2\sqrt{226}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{226}}{2*5}=\frac{2-2\sqrt{226}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{226}}{2*5}=\frac{2+2\sqrt{226}}{10} $
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