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3x+5(7-x)x=5
We move all terms to the left:
3x+5(7-x)x-(5)=0
We add all the numbers together, and all the variables
3x+5(-1x+7)x-5=0
We multiply parentheses
-5x^2+3x+35x-5=0
We add all the numbers together, and all the variables
-5x^2+38x-5=0
a = -5; b = 38; c = -5;
Δ = b2-4ac
Δ = 382-4·(-5)·(-5)
Δ = 1344
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-8\sqrt{21}}{2*-5}=\frac{-38-8\sqrt{21}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+8\sqrt{21}}{2*-5}=\frac{-38+8\sqrt{21}}{-10} $
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