(x+3)(x-10)=29

Solution for (x+3)(x-10)=29 equation:

(x+3)(x-10)=29

We move all terms to the left:

(x+3)(x-10)-(29)=0

We multiply parentheses ..

(+x^2-10x+3x-30)-29=0

We get rid of parentheses

x^2-10x+3x-30-29=0

We add all the numbers together, and all the variables

x^2-7x-59=0

a = 1; b = -7; c = -59;
Δ = b2-4ac
Δ = -72-4·1·(-59)
Δ = 285
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{-(-7)-\sqrt{285}}{2*1}=\frac{7-\sqrt{285}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{285}}{2*1}=\frac{7+\sqrt{285}}{2}
$