(35+x)(25+x)=1750

Solution for (35+x)(25+x)=1750 equation:

(35+x)(25+x)=1750

We move all terms to the left:

(35+x)(25+x)-(1750)=0

We add all the numbers together, and all the variables

(x+35)(x+25)-1750=0

We multiply parentheses ..

(+x^2+25x+35x+875)-1750=0

We get rid of parentheses

x^2+25x+35x+875-1750=0

We add all the numbers together, and all the variables

x^2+60x-875=0

a = 1; b = 60; c = -875;
Δ = b2-4ac
Δ = 602-4·1·(-875)
Δ = 7100
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:

$\sqrt{\Delta}=\sqrt{7100}=\sqrt{100*71}=\sqrt{100}*\sqrt{71}=10\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-10\sqrt{71}}{2*1}=\frac{-60-10\sqrt{71}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+10\sqrt{71}}{2*1}=\frac{-60+10\sqrt{71}}{2}
$