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6x+4x^2=91
We move all terms to the left:
6x+4x^2-(91)=0
a = 4; b = 6; c = -91;
Δ = b2-4ac
Δ = 62-4·4·(-91)
Δ = 1492
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1492}=\sqrt{4*373}=\sqrt{4}*\sqrt{373}=2\sqrt{373}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{373}}{2*4}=\frac{-6-2\sqrt{373}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{373}}{2*4}=\frac{-6+2\sqrt{373}}{8} $
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