x^2+10x+25=25/16

Solution for x^2+10x+25=25/16 equation:

x^2+10x+25=25/16

We move all terms to the left:

x^2+10x+25-(25/16)=0

We add all the numbers together, and all the variables

x^2+10x+25-(+25/16)=0

We get rid of parentheses

x^2+10x+25-25/16=0

We multiply all the terms by the denominator


x^2*16+10x*16-25+25*16=0

We add all the numbers together, and all the variables

x^2*16+10x*16+375=0

Wy multiply elements

16x^2+160x+375=0

a = 16; b = 160; c = +375;
Δ = b2-4ac
Δ = 1602-4·16·375
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(160)-40}{2*16}=\frac{-200}{32}
=-6+1/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(160)+40}{2*16}=\frac{-120}{32}
=-3+3/4
$