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3x^2-6x-30=45
We move all terms to the left:
3x^2-6x-30-(45)=0
We add all the numbers together, and all the variables
3x^2-6x-75=0
a = 3; b = -6; c = -75;
Δ = b2-4ac
Δ = -62-4·3·(-75)
Δ = 936
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-6\sqrt{26}}{2*3}=\frac{6-6\sqrt{26}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+6\sqrt{26}}{2*3}=\frac{6+6\sqrt{26}}{6} $
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