25x+43=(x-1)(5x+6)

Solution for 25x+43=(x-1)(5x+6) equation:

25x+43=(x-1)(5x+6)

We move all terms to the left:

25x+43-((x-1)(5x+6))=0

We multiply parentheses ..

-((+5x^2+6x-5x-6))+25x+43=0


We calculate terms in parentheses: -((+5x^2+6x-5x-6)), so:

(+5x^2+6x-5x-6)

We get rid of parentheses

5x^2+6x-5x-6

We add all the numbers together, and all the variables

5x^2+x-6

Back to the equation:

-(5x^2+x-6)


We add all the numbers together, and all the variables

25x-(5x^2+x-6)+43=0

We get rid of parentheses

-5x^2+25x-x+6+43=0

We add all the numbers together, and all the variables

-5x^2+24x+49=0

a = -5; b = 24; c = +49;
Δ = b2-4ac
Δ = 242-4·(-5)·49
Δ = 1556
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1556}=\sqrt{4*389}=\sqrt{4}*\sqrt{389}=2\sqrt{389}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{389}}{2*-5}=\frac{-24-2\sqrt{389}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{389}}{2*-5}=\frac{-24+2\sqrt{389}}{-10}
$