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3x(5x+1)=13x+3
We move all terms to the left:
3x(5x+1)-(13x+3)=0
We multiply parentheses
15x^2+3x-(13x+3)=0
We get rid of parentheses
15x^2+3x-13x-3=0
We add all the numbers together, and all the variables
15x^2-10x-3=0
a = 15; b = -10; c = -3;
Δ = b2-4ac
Δ = -102-4·15·(-3)
Δ = 280
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{70}}{2*15}=\frac{10-2\sqrt{70}}{30} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{70}}{2*15}=\frac{10+2\sqrt{70}}{30} $
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