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(2x+35)(3x-25)=250
We move all terms to the left:
(2x+35)(3x-25)-(250)=0
We multiply parentheses ..
(+6x^2-50x+105x-875)-250=0
We get rid of parentheses
6x^2-50x+105x-875-250=0
We add all the numbers together, and all the variables
6x^2+55x-1125=0
a = 6; b = 55; c = -1125;
Δ = b2-4ac
Δ = 552-4·6·(-1125)
Δ = 30025
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{30025}=\sqrt{25*1201}=\sqrt{25}*\sqrt{1201}=5\sqrt{1201}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-5\sqrt{1201}}{2*6}=\frac{-55-5\sqrt{1201}}{12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+5\sqrt{1201}}{2*6}=\frac{-55+5\sqrt{1201}}{12} $
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