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5x^2=12x+3
We move all terms to the left:
5x^2-(12x+3)=0
We get rid of parentheses
5x^2-12x-3=0
a = 5; b = -12; c = -3;
Δ = b2-4ac
Δ = -122-4·5·(-3)
Δ = 204
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{204}=\sqrt{4*51}=\sqrt{4}*\sqrt{51}=2\sqrt{51}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{51}}{2*5}=\frac{12-2\sqrt{51}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{51}}{2*5}=\frac{12+2\sqrt{51}}{10} $
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