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15x^2-(3x-1)=120
We move all terms to the left:
15x^2-(3x-1)-(120)=0
We get rid of parentheses
15x^2-3x+1-120=0
We add all the numbers together, and all the variables
15x^2-3x-119=0
a = 15; b = -3; c = -119;
Δ = b2-4ac
Δ = -32-4·15·(-119)
Δ = 7149
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{-(-3)-\sqrt{7149}}{2*15}=\frac{3-\sqrt{7149}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{7149}}{2*15}=\frac{3+\sqrt{7149}}{30} $
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