(8x+3)(2x-5)-(3x+5)(3x-5)=22x-10

Solution for (8x+3)(2x-5)-(3x+5)(3x-5)=22x-10 equation:

(8x+3)(2x-5)-(3x+5)(3x-5)=22x-10

We move all terms to the left:

(8x+3)(2x-5)-(3x+5)(3x-5)-(22x-10)=0

We use the square of the difference formula

9x^2+(8x+3)(2x-5)-(22x-10)+25=0

We get rid of parentheses

9x^2+(8x+3)(2x-5)-22x+10+25=0

We multiply parentheses ..

9x^2+(+16x^2-40x+6x-15)-22x+10+25=0

We add all the numbers together, and all the variables

9x^2+(+16x^2-40x+6x-15)-22x+35=0

We get rid of parentheses

9x^2+16x^2-40x+6x-22x-15+35=0

We add all the numbers together, and all the variables

25x^2-56x+20=0

a = 25; b = -56; c = +20;
Δ = b2-4ac
Δ = -562-4·25·20
Δ = 1136
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:

$\sqrt{\Delta}=\sqrt{1136}=\sqrt{16*71}=\sqrt{16}*\sqrt{71}=4\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-56)-4\sqrt{71}}{2*25}=\frac{56-4\sqrt{71}}{50}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-56)+4\sqrt{71}}{2*25}=\frac{56+4\sqrt{71}}{50}
$