4(x^2+23x-210)=0

Solution for 4(x^2+23x-210)=0 equation:

4(x^2+23x-210)=0

We multiply parentheses

4x^2+92x-840=0

a = 4; b = 92; c = -840;
Δ = b2-4ac
Δ = 922-4·4·(-840)
Δ = 21904
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{21904}=148$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(92)-148}{2*4}=\frac{-240}{8}
=-30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(92)+148}{2*4}=\frac{56}{8}
=7
$