(4x-1)(x+5)=2x+10(2x+7)

Solution for (4x-1)(x+5)=2x+10(2x+7) equation:

(4x-1)(x+5)=2x+10(2x+7)

We move all terms to the left:

(4x-1)(x+5)-(2x+10(2x+7))=0

We multiply parentheses ..

(+4x^2+20x-1x-5)-(2x+10(2x+7))=0


We calculate terms in parentheses: -(2x+10(2x+7)), so:

2x+10(2x+7)

We multiply parentheses

2x+20x+70

We add all the numbers together, and all the variables

22x+70

Back to the equation:

-(22x+70)


We get rid of parentheses

4x^2+20x-1x-22x-5-70=0

We add all the numbers together, and all the variables

4x^2-3x-75=0

a = 4; b = -3; c = -75;
Δ = b2-4ac
Δ = -32-4·4·(-75)
Δ = 1209
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{-(-3)-\sqrt{1209}}{2*4}=\frac{3-\sqrt{1209}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{1209}}{2*4}=\frac{3+\sqrt{1209}}{8}
$