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5x^2-10=192x-40
We move all terms to the left:
5x^2-10-(192x-40)=0
We get rid of parentheses
5x^2-192x+40-10=0
We add all the numbers together, and all the variables
5x^2-192x+30=0
a = 5; b = -192; c = +30;
Δ = b2-4ac
Δ = -1922-4·5·30
Δ = 36264
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{36264}=\sqrt{4*9066}=\sqrt{4}*\sqrt{9066}=2\sqrt{9066}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-2\sqrt{9066}}{2*5}=\frac{192-2\sqrt{9066}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+2\sqrt{9066}}{2*5}=\frac{192+2\sqrt{9066}}{10} $
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