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32x(x+18)+29x+3(x-5)=945
We move all terms to the left:
32x(x+18)+29x+3(x-5)-(945)=0
We add all the numbers together, and all the variables
29x+32x(x+18)+3(x-5)-945=0
We multiply parentheses
32x^2+29x+576x+3x-15-945=0
We add all the numbers together, and all the variables
32x^2+608x-960=0
a = 32; b = 608; c = -960;
Δ = b2-4ac
Δ = 6082-4·32·(-960)
Δ = 492544
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{492544}=\sqrt{1024*481}=\sqrt{1024}*\sqrt{481}=32\sqrt{481}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(608)-32\sqrt{481}}{2*32}=\frac{-608-32\sqrt{481}}{64} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(608)+32\sqrt{481}}{2*32}=\frac{-608+32\sqrt{481}}{64} $
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