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2(-x+4)5x-3=11
We move all terms to the left:
2(-x+4)5x-3-(11)=0
We add all the numbers together, and all the variables
2(-1x+4)5x-3-11=0
We add all the numbers together, and all the variables
2(-1x+4)5x-14=0
We multiply parentheses
-10x^2+40x-14=0
a = -10; b = 40; c = -14;
Δ = b2-4ac
Δ = 402-4·(-10)·(-14)
Δ = 1040
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-4\sqrt{65}}{2*-10}=\frac{-40-4\sqrt{65}}{-20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+4\sqrt{65}}{2*-10}=\frac{-40+4\sqrt{65}}{-20} $
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