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3x(4x+5)-5x=17
We move all terms to the left:
3x(4x+5)-5x-(17)=0
We add all the numbers together, and all the variables
-5x+3x(4x+5)-17=0
We multiply parentheses
12x^2-5x+15x-17=0
We add all the numbers together, and all the variables
12x^2+10x-17=0
a = 12; b = 10; c = -17;
Δ = b2-4ac
Δ = 102-4·12·(-17)
Δ = 916
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{916}=\sqrt{4*229}=\sqrt{4}*\sqrt{229}=2\sqrt{229}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{229}}{2*12}=\frac{-10-2\sqrt{229}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{229}}{2*12}=\frac{-10+2\sqrt{229}}{24} $
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