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5x^2=3/7
We move all terms to the left:
5x^2-(3/7)=0
We add all the numbers together, and all the variables
5x^2-(+3/7)=0
We get rid of parentheses
5x^2-3/7=0
We multiply all the terms by the denominator
5x^2*7-3=0
Wy multiply elements
35x^2-3=0
a = 35; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·35·(-3)
Δ = 420
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{105}}{2*35}=\frac{0-2\sqrt{105}}{70} =-\frac{2\sqrt{105}}{70} =-\frac{\sqrt{105}}{35} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{105}}{2*35}=\frac{0+2\sqrt{105}}{70} =\frac{2\sqrt{105}}{70} =\frac{\sqrt{105}}{35} $
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