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(2.5-x)(7.5-3x)=6x
We move all terms to the left:
(2.5-x)(7.5-3x)-(6x)=0
We add all the numbers together, and all the variables
(-1x+2.5)(-3x+7.5)-6x=0
We add all the numbers together, and all the variables
-6x+(-1x+2.5)(-3x+7.5)=0
We multiply parentheses ..
(+3x^2-7.5x-7.5x+18.75)-6x=0
We get rid of parentheses
3x^2-7.5x-7.5x-6x+18.75=0
We add all the numbers together, and all the variables
3x^2-21x+18.75=0
a = 3; b = -21; c = +18.75;
Δ = b2-4ac
Δ = -212-4·3·18.75
Δ = 216
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-6\sqrt{6}}{2*3}=\frac{21-6\sqrt{6}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+6\sqrt{6}}{2*3}=\frac{21+6\sqrt{6}}{6} $
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