(7x+5)(7x+5)=50

Solution for (7x+5)(7x+5)=50 equation:

(7x+5)(7x+5)=50

We move all terms to the left:

(7x+5)(7x+5)-(50)=0

We multiply parentheses ..

(+49x^2+35x+35x+25)-50=0

We get rid of parentheses

49x^2+35x+35x+25-50=0

We add all the numbers together, and all the variables

49x^2+70x-25=0

a = 49; b = 70; c = -25;
Δ = b2-4ac
Δ = 702-4·49·(-25)
Δ = 9800
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:

$\sqrt{\Delta}=\sqrt{9800}=\sqrt{4900*2}=\sqrt{4900}*\sqrt{2}=70\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(70)-70\sqrt{2}}{2*49}=\frac{-70-70\sqrt{2}}{98}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(70)+70\sqrt{2}}{2*49}=\frac{-70+70\sqrt{2}}{98}
$