(9x-25)(10x+8)=26

Solution for (9x-25)(10x+8)=26 equation:

(9x-25)(10x+8)=26

We move all terms to the left:

(9x-25)(10x+8)-(26)=0

We multiply parentheses ..

(+90x^2+72x-250x-200)-26=0

We get rid of parentheses

90x^2+72x-250x-200-26=0

We add all the numbers together, and all the variables

90x^2-178x-226=0

a = 90; b = -178; c = -226;
Δ = b2-4ac
Δ = -1782-4·90·(-226)
Δ = 113044
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:

$\sqrt{\Delta}=\sqrt{113044}=\sqrt{4*28261}=\sqrt{4}*\sqrt{28261}=2\sqrt{28261}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-178)-2\sqrt{28261}}{2*90}=\frac{178-2\sqrt{28261}}{180}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-178)+2\sqrt{28261}}{2*90}=\frac{178+2\sqrt{28261}}{180}
$