683=-16x^2+176x+235

Solution for 683=-16x^2+176x+235 equation:

683=-16x^2+176x+235

We move all terms to the left:

683-(-16x^2+176x+235)=0

We get rid of parentheses

16x^2-176x-235+683=0

We add all the numbers together, and all the variables

16x^2-176x+448=0

a = 16; b = -176; c = +448;
Δ = b2-4ac
Δ = -1762-4·16·448
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-176)-48}{2*16}=\frac{128}{32}
=4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-176)+48}{2*16}=\frac{224}{32}
=7
$