(x+1)(2x-15)=10

Solution for (x+1)(2x-15)=10 equation:

(x+1)(2x-15)=10

We move all terms to the left:

(x+1)(2x-15)-(10)=0

We multiply parentheses ..

(+2x^2-15x+2x-15)-10=0

We get rid of parentheses

2x^2-15x+2x-15-10=0

We add all the numbers together, and all the variables

2x^2-13x-25=0

a = 2; b = -13; c = -25;
Δ = b2-4ac
Δ = -132-4·2·(-25)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-3\sqrt{41}}{2*2}=\frac{13-3\sqrt{41}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+3\sqrt{41}}{2*2}=\frac{13+3\sqrt{41}}{4}
$