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3x*5x-4=36
We move all terms to the left:
3x*5x-4-(36)=0
We add all the numbers together, and all the variables
3x*5x-40=0
Wy multiply elements
15x^2-40=0
a = 15; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·15·(-40)
Δ = 2400
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{6}}{2*15}=\frac{0-20\sqrt{6}}{30} =-\frac{20\sqrt{6}}{30} =-\frac{2\sqrt{6}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{6}}{2*15}=\frac{0+20\sqrt{6}}{30} =\frac{20\sqrt{6}}{30} =\frac{2\sqrt{6}}{3} $
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