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x^2=7-24/7
We move all terms to the left:
x^2-(7-24/7)=0
We add all the numbers together, and all the variables
x^2-(-24/7+7)=0
We get rid of parentheses
x^2-7+24/7=0
We multiply all the terms by the denominator
x^2*7+24-7*7=0
We add all the numbers together, and all the variables
x^2*7-25=0
Wy multiply elements
7x^2-25=0
a = 7; b = 0; c = -25;
Δ = b2-4ac
Δ = 02-4·7·(-25)
Δ = 700
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{7}}{2*7}=\frac{0-10\sqrt{7}}{14} =-\frac{10\sqrt{7}}{14} =-\frac{5\sqrt{7}}{7} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{7}}{2*7}=\frac{0+10\sqrt{7}}{14} =\frac{10\sqrt{7}}{14} =\frac{5\sqrt{7}}{7} $
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