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2x+2x(5/7x)=262.5
We move all terms to the left:
2x+2x(5/7x)-(262.5)=0
Domain of the equation: 7x)!=0We add all the numbers together, and all the variables
x!=0/1
x!=0
x∈R
2x+2x(+5/7x)-(262.5)=0
We add all the numbers together, and all the variables
2x+2x(+5/7x)-262.5=0
We multiply parentheses
10x^2+2x-262.5=0
a = 10; b = 2; c = -262.5;
Δ = b2-4ac
Δ = 22-4·10·(-262.5)
Δ = 10504
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10504}=\sqrt{4*2626}=\sqrt{4}*\sqrt{2626}=2\sqrt{2626}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{2626}}{2*10}=\frac{-2-2\sqrt{2626}}{20} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{2626}}{2*10}=\frac{-2+2\sqrt{2626}}{20} $
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