4x^2+90x+306=0

Solution for 4x^2+90x+306=0 equation:

4x^2+90x+306=0

a = 4; b = 90; c = +306;
Δ = b2-4ac
Δ = 902-4·4·306
Δ = 3204
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:

$\sqrt{\Delta}=\sqrt{3204}=\sqrt{36*89}=\sqrt{36}*\sqrt{89}=6\sqrt{89}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(90)-6\sqrt{89}}{2*4}=\frac{-90-6\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(90)+6\sqrt{89}}{2*4}=\frac{-90+6\sqrt{89}}{8}
$