(70-2x)(30-2x)-5800=0

Solution for (70-2x)(30-2x)-5800=0 equation:

(70-2x)(30-2x)-5800=0

We add all the numbers together, and all the variables

(-2x+70)(-2x+30)-5800=0

We multiply parentheses ..

(+4x^2-60x-140x+2100)-5800=0

We get rid of parentheses

4x^2-60x-140x+2100-5800=0

We add all the numbers together, and all the variables

4x^2-200x-3700=0

a = 4; b = -200; c = -3700;
Δ = b2-4ac
Δ = -2002-4·4·(-3700)
Δ = 99200
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:

$\sqrt{\Delta}=\sqrt{99200}=\sqrt{1600*62}=\sqrt{1600}*\sqrt{62}=40\sqrt{62}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-40\sqrt{62}}{2*4}=\frac{200-40\sqrt{62}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+40\sqrt{62}}{2*4}=\frac{200+40\sqrt{62}}{8}
$