4x^2+34x-21=0

Solution for 4x^2+34x-21=0 equation:

4x^2+34x-21=0

a = 4; b = 34; c = -21;
Δ = b2-4ac
Δ = 342-4·4·(-21)
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{-(34)-2\sqrt{373}}{2*4}=\frac{-34-2\sqrt{373}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{373}}{2*4}=\frac{-34+2\sqrt{373}}{8}
$