(c+5)(2c-7)=123

Solution for (c+5)(2c-7)=123 equation:

(c+5)(2c-7)=123

We move all terms to the left:

(c+5)(2c-7)-(123)=0

We multiply parentheses ..

(+2c^2-7c+10c-35)-123=0

We get rid of parentheses

2c^2-7c+10c-35-123=0

We add all the numbers together, and all the variables

2c^2+3c-158=0

a = 2; b = 3; c = -158;
Δ = b2-4ac
Δ = 32-4·2·(-158)
Δ = 1273
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$c_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{1273}}{2*2}=\frac{-3-\sqrt{1273}}{4}
$
$c_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{1273}}{2*2}=\frac{-3+\sqrt{1273}}{4}
$