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x^2+0.75x^2=841
We move all terms to the left:
x^2+0.75x^2-(841)=0
We add all the numbers together, and all the variables
1.75x^2-841=0
a = 1.75; b = 0; c = -841;
Δ = b2-4ac
Δ = 02-4·1.75·(-841)
Δ = 5887
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5887}=\sqrt{841*7}=\sqrt{841}*\sqrt{7}=29\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-29\sqrt{7}}{2*1.75}=\frac{0-29\sqrt{7}}{3.5} =-\frac{29\sqrt{7}}{3.5} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+29\sqrt{7}}{2*1.75}=\frac{0+29\sqrt{7}}{3.5} =\frac{29\sqrt{7}}{3.5} $
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