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3x(x+5)-(x-5)=0
We multiply parentheses
3x^2+15x-(x-5)=0
We get rid of parentheses
3x^2+15x-x+5=0
We add all the numbers together, and all the variables
3x^2+14x+5=0
a = 3; b = 14; c = +5;
Δ = b2-4ac
Δ = 142-4·3·5
Δ = 136
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{34}}{2*3}=\frac{-14-2\sqrt{34}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{34}}{2*3}=\frac{-14+2\sqrt{34}}{6} $
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