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55-3x*10x+23=8x+12
We move all terms to the left:
55-3x*10x+23-(8x+12)=0
We add all the numbers together, and all the variables
-3x*10x-(8x+12)+78=0
Wy multiply elements
-30x^2-(8x+12)+78=0
We get rid of parentheses
-30x^2-8x-12+78=0
We add all the numbers together, and all the variables
-30x^2-8x+66=0
a = -30; b = -8; c = +66;
Δ = b2-4ac
Δ = -82-4·(-30)·66
Δ = 7984
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7984}=\sqrt{16*499}=\sqrt{16}*\sqrt{499}=4\sqrt{499}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{499}}{2*-30}=\frac{8-4\sqrt{499}}{-60} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{499}}{2*-30}=\frac{8+4\sqrt{499}}{-60} $
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