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5x^2=15x-2/5
We move all terms to the left:
5x^2-(15x-2/5)=0
We add all the numbers together, and all the variables
5x^2-(+15x-2/5)=0
We get rid of parentheses
5x^2-15x+2/5=0
We multiply all the terms by the denominator
5x^2*5-15x*5+2=0
Wy multiply elements
25x^2-75x+2=0
a = 25; b = -75; c = +2;
Δ = b2-4ac
Δ = -752-4·25·2
Δ = 5425
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{5425}=\sqrt{25*217}=\sqrt{25}*\sqrt{217}=5\sqrt{217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{217}}{2*25}=\frac{75-5\sqrt{217}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{217}}{2*25}=\frac{75+5\sqrt{217}}{50} $
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