(x-2)*(x+5)=9x+10

Solution for (x-2)*(x+5)=9x+10 equation:

(x-2)(x+5)=9x+10

We move all terms to the left:

(x-2)(x+5)-(9x+10)=0

We get rid of parentheses

(x-2)(x+5)-9x-10=0

We multiply parentheses ..

(+x^2+5x-2x-10)-9x-10=0

We get rid of parentheses

x^2+5x-2x-9x-10-10=0

We add all the numbers together, and all the variables

x^2-6x-20=0

a = 1; b = -6; c = -20;
Δ = b2-4ac
Δ = -62-4·1·(-20)
Δ = 116
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:

$\sqrt{\Delta}=\sqrt{116}=\sqrt{4*29}=\sqrt{4}*\sqrt{29}=2\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{29}}{2*1}=\frac{6-2\sqrt{29}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{29}}{2*1}=\frac{6+2\sqrt{29}}{2}
$