(4x-1)(x+4)=10

Solution for (4x-1)(x+4)=10 equation:

(4x-1)(x+4)=10

We move all terms to the left:

(4x-1)(x+4)-(10)=0

We multiply parentheses ..

(+4x^2+16x-1x-4)-10=0

We get rid of parentheses

4x^2+16x-1x-4-10=0

We add all the numbers together, and all the variables

4x^2+15x-14=0

a = 4; b = 15; c = -14;
Δ = b2-4ac
Δ = 152-4·4·(-14)
Δ = 449
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{-(15)-\sqrt{449}}{2*4}=\frac{-15-\sqrt{449}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{449}}{2*4}=\frac{-15+\sqrt{449}}{8}
$