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4x+7x^2=6
We move all terms to the left:
4x+7x^2-(6)=0
a = 7; b = 4; c = -6;
Δ = b2-4ac
Δ = 42-4·7·(-6)
Δ = 184
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{46}}{2*7}=\frac{-4-2\sqrt{46}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{46}}{2*7}=\frac{-4+2\sqrt{46}}{14} $
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