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5x^2+13x-10=x
We move all terms to the left:
5x^2+13x-10-(x)=0
We add all the numbers together, and all the variables
5x^2+12x-10=0
a = 5; b = 12; c = -10;
Δ = b2-4ac
Δ = 122-4·5·(-10)
Δ = 344
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{344}=\sqrt{4*86}=\sqrt{4}*\sqrt{86}=2\sqrt{86}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{86}}{2*5}=\frac{-12-2\sqrt{86}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{86}}{2*5}=\frac{-12+2\sqrt{86}}{10} $
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