(2x-3)(x+5)=10

Solution for (2x-3)(x+5)=10 equation:

(2x-3)(x+5)=10

We move all terms to the left:

(2x-3)(x+5)-(10)=0

We multiply parentheses ..

(+2x^2+10x-3x-15)-10=0

We get rid of parentheses

2x^2+10x-3x-15-10=0

We add all the numbers together, and all the variables

2x^2+7x-25=0

a = 2; b = 7; c = -25;
Δ = b2-4ac
Δ = 72-4·2·(-25)
Δ = 249
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{249}}{2*2}=\frac{-7-\sqrt{249}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{249}}{2*2}=\frac{-7+\sqrt{249}}{4}
$