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55-3x*8x+12*10x+23=0
We add all the numbers together, and all the variables
-3x*8x+12*10x+78=0
Wy multiply elements
-24x^2+120x+78=0
a = -24; b = 120; c = +78;
Δ = b2-4ac
Δ = 1202-4·(-24)·78
Δ = 21888
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{21888}=\sqrt{576*38}=\sqrt{576}*\sqrt{38}=24\sqrt{38}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-24\sqrt{38}}{2*-24}=\frac{-120-24\sqrt{38}}{-48} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+24\sqrt{38}}{2*-24}=\frac{-120+24\sqrt{38}}{-48} $
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