144x^2+4x-3=0

Solution for 144x^2+4x-3=0 equation:

144x^2+4x-3=0

a = 144; b = 4; c = -3;
Δ = b2-4ac
Δ = 42-4·144·(-3)
Δ = 1744
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:

$\sqrt{\Delta}=\sqrt{1744}=\sqrt{16*109}=\sqrt{16}*\sqrt{109}=4\sqrt{109}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-4\sqrt{109}}{2*144}=\frac{-4-4\sqrt{109}}{288}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+4\sqrt{109}}{2*144}=\frac{-4+4\sqrt{109}}{288}
$