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5x^2-13x-27=8-x
We move all terms to the left:
5x^2-13x-27-(8-x)=0
We add all the numbers together, and all the variables
5x^2-13x-(-1x+8)-27=0
We get rid of parentheses
5x^2-13x+1x-8-27=0
We add all the numbers together, and all the variables
5x^2-12x-35=0
a = 5; b = -12; c = -35;
Δ = b2-4ac
Δ = -122-4·5·(-35)
Δ = 844
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{844}=\sqrt{4*211}=\sqrt{4}*\sqrt{211}=2\sqrt{211}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{211}}{2*5}=\frac{12-2\sqrt{211}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{211}}{2*5}=\frac{12+2\sqrt{211}}{10} $
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