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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+4x^2-40x+5x-50)-((2x+7)2)=0


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

(2x+7)2

We multiply parentheses

4x+14

Back to the equation:

-(4x+14)


We get rid of parentheses

4x^2-40x+5x-4x-50-14=0

We add all the numbers together, and all the variables

4x^2-39x-64=0

a = 4; b = -39; c = -64;
Δ = b2-4ac
Δ = -392-4·4·(-64)
Δ = 2545
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{-(-39)-\sqrt{2545}}{2*4}=\frac{39-\sqrt{2545}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+\sqrt{2545}}{2*4}=\frac{39+\sqrt{2545}}{8}
$