(14x2)+6x=76

Solution for (14x2)+6x=76 equation:

(14x^2)+6x=76

We move all terms to the left:

(14x^2)+6x-(76)=0

a = 14; b = 6; c = -76;
Δ = b2-4ac
Δ = 62-4·14·(-76)
Δ = 4292
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:

$\sqrt{\Delta}=\sqrt{4292}=\sqrt{4*1073}=\sqrt{4}*\sqrt{1073}=2\sqrt{1073}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{1073}}{2*14}=\frac{-6-2\sqrt{1073}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{1073}}{2*14}=\frac{-6+2\sqrt{1073}}{28}
$