43x^2+29x-140=0

Solution for 43x^2+29x-140=0 equation:

43x^2+29x-140=0

a = 43; b = 29; c = -140;
Δ = b2-4ac
Δ = 292-4·43·(-140)
Δ = 24921
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:

$\sqrt{\Delta}=\sqrt{24921}=\sqrt{9*2769}=\sqrt{9}*\sqrt{2769}=3\sqrt{2769}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-3\sqrt{2769}}{2*43}=\frac{-29-3\sqrt{2769}}{86}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+3\sqrt{2769}}{2*43}=\frac{-29+3\sqrt{2769}}{86}
$