2x(x-5)+3(x+1)=32

Solution for 2x(x-5)+3(x+1)=32 equation:

2x(x-5)+3(x+1)=32

We move all terms to the left:

2x(x-5)+3(x+1)-(32)=0

We multiply parentheses

2x^2-10x+3x+3-32=0

We add all the numbers together, and all the variables

2x^2-7x-29=0

a = 2; b = -7; c = -29;
Δ = b2-4ac
Δ = -72-4·2·(-29)
Δ = 281
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{281}}{2*2}=\frac{7-\sqrt{281}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{281}}{2*2}=\frac{7+\sqrt{281}}{4}
$