(5x-3)(5x-3)=49

Solution for (5x-3)(5x-3)=49 equation:

(5x-3)(5x-3)=49

We move all terms to the left:

(5x-3)(5x-3)-(49)=0

We multiply parentheses ..

(+25x^2-15x-15x+9)-49=0

We get rid of parentheses

25x^2-15x-15x+9-49=0

We add all the numbers together, and all the variables

25x^2-30x-40=0

a = 25; b = -30; c = -40;
Δ = b2-4ac
Δ = -302-4·25·(-40)
Δ = 4900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4900}=70$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-70}{2*25}=\frac{-40}{50}
=-4/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+70}{2*25}=\frac{100}{50}
=2
$