0.25x+7=4x(x-2)

Solution for 0.25x+7=4x(x-2) equation:

0.25x+7=4x(x-2)

We move all terms to the left:

0.25x+7-(4x(x-2))=0


We calculate terms in parentheses: -(4x(x-2)), so:

4x(x-2)

We multiply parentheses

4x^2-8x

Back to the equation:

-(4x^2-8x)


We get rid of parentheses

-4x^2+0.25x+8x+7=0

We add all the numbers together, and all the variables

-4x^2+8.25x+7=0

a = -4; b = 8.25; c = +7;
Δ = b2-4ac
Δ = 8.252-4·(-4)·7
Δ = 180.0625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8.25)-\sqrt{180.0625}}{2*-4}=\frac{-8.25-\sqrt{180.0625}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8.25)+\sqrt{180.0625}}{2*-4}=\frac{-8.25+\sqrt{180.0625}}{-8}
$