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2+x(3x+8-1)=45
We move all terms to the left:
2+x(3x+8-1)-(45)=0
We add all the numbers together, and all the variables
x(3x+7)+2-45=0
We add all the numbers together, and all the variables
x(3x+7)-43=0
We multiply parentheses
3x^2+7x-43=0
a = 3; b = 7; c = -43;
Δ = b2-4ac
Δ = 72-4·3·(-43)
Δ = 565
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{-(7)-\sqrt{565}}{2*3}=\frac{-7-\sqrt{565}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{565}}{2*3}=\frac{-7+\sqrt{565}}{6} $
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