(x)=4x2+3x-25

Solution for (x)=4x2+3x-25 equation:

(x)=4x^2+3x-25

We move all terms to the left:

(x)-(4x^2+3x-25)=0

We get rid of parentheses

-4x^2+x-3x+25=0

We add all the numbers together, and all the variables

-4x^2-2x+25=0

a = -4; b = -2; c = +25;
Δ = b2-4ac
Δ = -22-4·(-4)·25
Δ = 404
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:

$\sqrt{\Delta}=\sqrt{404}=\sqrt{4*101}=\sqrt{4}*\sqrt{101}=2\sqrt{101}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{101}}{2*-4}=\frac{2-2\sqrt{101}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{101}}{2*-4}=\frac{2+2\sqrt{101}}{-8}
$