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25=6x^2+75x+200
We move all terms to the left:
25-(6x^2+75x+200)=0
We get rid of parentheses
-6x^2-75x-200+25=0
We add all the numbers together, and all the variables
-6x^2-75x-175=0
a = -6; b = -75; c = -175;
Δ = b2-4ac
Δ = -752-4·(-6)·(-175)
Δ = 1425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1425}=\sqrt{25*57}=\sqrt{25}*\sqrt{57}=5\sqrt{57}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{57}}{2*-6}=\frac{75-5\sqrt{57}}{-12} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{57}}{2*-6}=\frac{75+5\sqrt{57}}{-12} $
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