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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-5x^2+4x+49=0

a = -5; b = 4; c = +49;
Δ = b2-4ac
Δ = 42-4·(-5)·49
Δ = 996
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:

$\sqrt{\Delta}=\sqrt{996}=\sqrt{4*249}=\sqrt{4}*\sqrt{249}=2\sqrt{249}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{249}}{2*-5}=\frac{-4-2\sqrt{249}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{249}}{2*-5}=\frac{-4+2\sqrt{249}}{-10}
$