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6x+15=4x^2
We move all terms to the left:
6x+15-(4x^2)=0
determiningTheFunctionDomain -4x^2+6x+15=0
a = -4; b = 6; c = +15;
Δ = b2-4ac
Δ = 62-4·(-4)·15
Δ = 276
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{276}=\sqrt{4*69}=\sqrt{4}*\sqrt{69}=2\sqrt{69}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{69}}{2*-4}=\frac{-6-2\sqrt{69}}{-8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{69}}{2*-4}=\frac{-6+2\sqrt{69}}{-8} $
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