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4x+6=5x^2
We move all terms to the left:
4x+6-(5x^2)=0
determiningTheFunctionDomain -5x^2+4x+6=0
a = -5; b = 4; c = +6;
Δ = b2-4ac
Δ = 42-4·(-5)·6
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{-(4)-2\sqrt{34}}{2*-5}=\frac{-4-2\sqrt{34}}{-10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{34}}{2*-5}=\frac{-4+2\sqrt{34}}{-10} $
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