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5(x-3)5x=-15=13
We move all terms to the left:
5(x-3)5x-(-15)=0
We add all the numbers together, and all the variables
5(x-3)5x+15=0
We multiply parentheses
25x^2-75x+15=0
a = 25; b = -75; c = +15;
Δ = b2-4ac
Δ = -752-4·25·15
Δ = 4125
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{4125}=\sqrt{25*165}=\sqrt{25}*\sqrt{165}=5\sqrt{165}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-75)-5\sqrt{165}}{2*25}=\frac{75-5\sqrt{165}}{50} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-75)+5\sqrt{165}}{2*25}=\frac{75+5\sqrt{165}}{50} $
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