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(3x-1)(5x+4)-30x=17
We move all terms to the left:
(3x-1)(5x+4)-30x-(17)=0
We add all the numbers together, and all the variables
-30x+(3x-1)(5x+4)-17=0
We multiply parentheses ..
(+15x^2+12x-5x-4)-30x-17=0
We get rid of parentheses
15x^2+12x-5x-30x-4-17=0
We add all the numbers together, and all the variables
15x^2-23x-21=0
a = 15; b = -23; c = -21;
Δ = b2-4ac
Δ = -232-4·15·(-21)
Δ = 1789
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{-(-23)-\sqrt{1789}}{2*15}=\frac{23-\sqrt{1789}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{1789}}{2*15}=\frac{23+\sqrt{1789}}{30} $
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