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7=3x*5x
We move all terms to the left:
7-(3x*5x)=0
We add all the numbers together, and all the variables
-(+3x*5x)+7=0
We get rid of parentheses
-3x*5x+7=0
Wy multiply elements
-15x^2+7=0
a = -15; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-15)·7
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*-15}=\frac{0-2\sqrt{105}}{-30} =-\frac{2\sqrt{105}}{-30} =-\frac{\sqrt{105}}{-15} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{105}}{2*-15}=\frac{0+2\sqrt{105}}{-30} =\frac{2\sqrt{105}}{-30} =\frac{\sqrt{105}}{-15} $
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