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89(5x-8)(3x+4)+51=360
We move all terms to the left:
89(5x-8)(3x+4)+51-(360)=0
We add all the numbers together, and all the variables
89(5x-8)(3x+4)-309=0
We multiply parentheses ..
89(+15x^2+20x-24x-32)-309=0
We multiply parentheses
1335x^2+1780x-2136x-2848-309=0
We add all the numbers together, and all the variables
1335x^2-356x-3157=0
a = 1335; b = -356; c = -3157;
Δ = b2-4ac
Δ = -3562-4·1335·(-3157)
Δ = 16985116
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{16985116}=\sqrt{4*4246279}=\sqrt{4}*\sqrt{4246279}=2\sqrt{4246279}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-356)-2\sqrt{4246279}}{2*1335}=\frac{356-2\sqrt{4246279}}{2670} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-356)+2\sqrt{4246279}}{2*1335}=\frac{356+2\sqrt{4246279}}{2670} $
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