(2u+7)(u-5)=0

Solution for (2u+7)(u-5)=0 equation:

(2u+7)(u-5)=0

We multiply parentheses ..

(+2u^2-10u+7u-35)=0

We get rid of parentheses

2u^2-10u+7u-35=0

We add all the numbers together, and all the variables

2u^2-3u-35=0

a = 2; b = -3; c = -35;
Δ = b2-4ac
Δ = -32-4·2·(-35)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$u_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-17}{2*2}=\frac{-14}{4}
=-3+1/2
$
$u_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+17}{2*2}=\frac{20}{4}
=5
$