(34-x)*(23-x)+260=782

Solution for (34-x)*(23-x)+260=782 equation:

(34-x)(23-x)+260=782

We move all terms to the left:

(34-x)(23-x)+260-(782)=0

We add all the numbers together, and all the variables

(-1x+34)(-1x+23)+260-782=0

We add all the numbers together, and all the variables

(-1x+34)(-1x+23)-522=0

We multiply parentheses ..

(+x^2-23x-34x+782)-522=0

We get rid of parentheses

x^2-23x-34x+782-522=0

We add all the numbers together, and all the variables

x^2-57x+260=0

a = 1; b = -57; c = +260;
Δ = b2-4ac
Δ = -572-4·1·260
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-57)-47}{2*1}=\frac{10}{2}
=5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-57)+47}{2*1}=\frac{104}{2}
=52
$