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3x(8.4-x)=25.2-3x
We move all terms to the left:
3x(8.4-x)-(25.2-3x)=0
We add all the numbers together, and all the variables
3x(-1x+8.4)-(-3x+25.2)=0
We multiply parentheses
-3x^2+25.2x-(-3x+25.2)=0
We get rid of parentheses
-3x^2+25.2x+3x-25.2=0
We add all the numbers together, and all the variables
-3x^2+28.2x-25.2=0
a = -3; b = 28.2; c = -25.2;
Δ = b2-4ac
Δ = 28.22-4·(-3)·(-25.2)
Δ = 492.84
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28.2)-\sqrt{492.84}}{2*-3}=\frac{-28.2-\sqrt{492.84}}{-6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28.2)+\sqrt{492.84}}{2*-3}=\frac{-28.2+\sqrt{492.84}}{-6} $
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