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4x-4x^2+100-250+36x-45x^2=-234
We move all terms to the left:
4x-4x^2+100-250+36x-45x^2-(-234)=0
We add all the numbers together, and all the variables
-49x^2+40x+84=0
a = -49; b = 40; c = +84;
Δ = b2-4ac
Δ = 402-4·(-49)·84
Δ = 18064
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{18064}=\sqrt{16*1129}=\sqrt{16}*\sqrt{1129}=4\sqrt{1129}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{1129}}{2*-49}=\frac{-40-4\sqrt{1129}}{-98} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{1129}}{2*-49}=\frac{-40+4\sqrt{1129}}{-98} $
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