(5+2t)(7+2t)=175

Solution for (5+2t)(7+2t)=175 equation:

(5+2t)(7+2t)=175

We move all terms to the left:

(5+2t)(7+2t)-(175)=0

We add all the numbers together, and all the variables

(2t+5)(2t+7)-175=0

We multiply parentheses ..

(+4t^2+14t+10t+35)-175=0

We get rid of parentheses

4t^2+14t+10t+35-175=0

We add all the numbers together, and all the variables

4t^2+24t-140=0

a = 4; b = 24; c = -140;
Δ = b2-4ac
Δ = 242-4·4·(-140)
Δ = 2816
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2816}=\sqrt{256*11}=\sqrt{256}*\sqrt{11}=16\sqrt{11}$
$t_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-16\sqrt{11}}{2*4}=\frac{-24-16\sqrt{11}}{8}
$
$t_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+16\sqrt{11}}{2*4}=\frac{-24+16\sqrt{11}}{8}
$