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25(3x-63)(x-52)=819000
We move all terms to the left:
25(3x-63)(x-52)-(819000)=0
We multiply parentheses ..
25(+3x^2-156x-63x+3276)-819000=0
We multiply parentheses
75x^2-3900x-1575x+81900-819000=0
We add all the numbers together, and all the variables
75x^2-5475x-737100=0
a = 75; b = -5475; c = -737100;
Δ = b2-4ac
Δ = -54752-4·75·(-737100)
Δ = 251105625
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{251105625}=\sqrt{5625*44641}=\sqrt{5625}*\sqrt{44641}=75\sqrt{44641}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5475)-75\sqrt{44641}}{2*75}=\frac{5475-75\sqrt{44641}}{150} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5475)+75\sqrt{44641}}{2*75}=\frac{5475+75\sqrt{44641}}{150} $
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