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5(x-3)+x2=27
We move all terms to the left:
5(x-3)+x2-(27)=0
We add all the numbers together, and all the variables
x^2+5(x-3)-27=0
We multiply parentheses
x^2+5x-15-27=0
We add all the numbers together, and all the variables
x^2+5x-42=0
a = 1; b = 5; c = -42;
Δ = b2-4ac
Δ = 52-4·1·(-42)
Δ = 193
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{-(5)-\sqrt{193}}{2*1}=\frac{-5-\sqrt{193}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{193}}{2*1}=\frac{-5+\sqrt{193}}{2} $
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