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4x^2+50x-300=846
We move all terms to the left:
4x^2+50x-300-(846)=0
We add all the numbers together, and all the variables
4x^2+50x-1146=0
a = 4; b = 50; c = -1146;
Δ = b2-4ac
Δ = 502-4·4·(-1146)
Δ = 20836
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{20836}=\sqrt{4*5209}=\sqrt{4}*\sqrt{5209}=2\sqrt{5209}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(50)-2\sqrt{5209}}{2*4}=\frac{-50-2\sqrt{5209}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(50)+2\sqrt{5209}}{2*4}=\frac{-50+2\sqrt{5209}}{8} $
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