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x^2-30=6-5x
We move all terms to the left:
x^2-30-(6-5x)=0
We add all the numbers together, and all the variables
x^2-(-5x+6)-30=0
We get rid of parentheses
x^2+5x-6-30=0
We add all the numbers together, and all the variables
x^2+5x-36=0
a = 1; b = 5; c = -36;
Δ = b2-4ac
Δ = 52-4·1·(-36)
Δ = 169
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{169}=13$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-13}{2*1}=\frac{-18}{2} =-9 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+13}{2*1}=\frac{8}{2} =4 $
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